Alexander Zimmermann's list of publications

Click here for (partially older) electronic versions of some of my papers on David Benson's preprint server.

Click here to see recent changes

  1. DG-Semiprimary DG-Algebras, Acyclicity and Hopkins-Levitzki Theorem for DG-Algebras to appear in Osaka Journal of Mathematics; preprint 9 pages; February 20, 2025 pdf ; arxiv ; HAL ;
  2. Dg-separable dg-extensions preprint 9 pages; December 2, 2024 pdf ; arxiv ; HAL ;
  3. Differential graded division algebras, their modules, and dg-simple algebras preprint August 8, 2024; 15 pages; to appear in Mathematica (Cluj) pdf ; HAL ; arxiv
    The strange condition in Theorem 2.4 on the set of homogeneous left regular elements and right regular elements is not necessary by a more careful argument. There one uses that a dg-division algebra does not have neither proper dg-left ideals nor proper dg-right ideals. See here for the proof and a nice example.
  4. On the Ring Theory of Differential Graded Rings preprint April 24, 2024; Oberwolfach Workshop Report 2416 pdf ;
  5. Ore Localisation for differential graded rings; Towards Goldie's theorem for differential graded algebras Journal of Algebra 663 (2025) 48-80. pdf ; arxiv ; HAL DOI
  6. Differential graded Brauer groups Revista de la Union Matematica Argentina 68 (no 1) (2025) 297-308. pdf ; DOI ; arxiv ; HAL
  7. Differential graded orders, their class groups and idèles preprint December 30, 2022; revised January 9, 2023; and September 10, 2024; 36 pages pdf , arxiv ; HAL ;
  8. Clifford's theorem for orbit categories preprint December 3, 2021; revised January 16, 2023; 21 pages; 28 pages in the journal; Applied Categorical Structures 31, volume 3; (2023) Article 17. read only https://doi.org/10.1007/s10485-023-09721-4
    pdf ; arXiv ; HAL ;
    Note (April 6, 2023): Angel del Rio mentioned a typo in Remark 3.1: Their example is in characteristic 2.
  9. Characters of Groups and Lattices over Orders; From Ordinary to Integral Representation Theory
    ivx + 358 pages; textbook submitted July 21, 2021 as de Gruyter textbook; to appear 19 January 2022 (electronic) and 2 Febraury 2022 (paperback)
  10. Remarks on a triangulated version of Auslander-Kleiner's Green correspondence proceedings of the 60th birthday volume of Sri Wahyuni; Southeast Asian Bulletin of Mathematics 45 (no 3) (2021) 409-427; pdf ; HAL ;
  11. On Equivalences Between Categories Of Representations 17 pages; 30 July, 2019; in the SEAMS (South East Asian Mathematical Society) conference proceedings; Yogyakarta, Indonesia, 29 July to 2 August 2019; AIP Conference Proceedings 2192, 020002 (2019): doi https://doi.org/10.1063/1.5139120; published online 19 December 2019. pdf ; HAL ;
  12. Green Correspondence and Relative Projectivity for Pairs of Adjoint Functors Between Triangulated Categories preprint first version May 3, 2019; revised January 14 and January 28, 2020; Pacific Journal of Mathematics 308-2 (2020), 473-509; DOI 10.2140/pjm.2020.308.473; pdf ; arXiv ; HAL ;
  13. with Manuel Saorin; Degenerating $0$ in Triangulated Categories 8 pages; 17 January 2020; pdf ; Nagoya Mathematical Journal 244 (2021), 158-167. DOI: 10.1017/nmj.2020.10
    initially submitted version pdf ; arXiv
  14. with Intan Muchtadi-Alamsyah and Adit Purwa Santika; Derived invariance of the subspaces of $p$-singular class sums in blocks 13 pages, March 2017; pdf ;
  15. with Manuel Saorin; Symmetry of the Definition of Degeneration in Triangulated Categories Algebras and Representation Theory 22 (2019) 801-836. dvi ; pdf ; arXiv ; HAL ; online view
  16. Külshammer ideals of algebras of quaternion type 26 pages, May 2016; revision January 2017; second revision May 2017; Journal of Algebra and its applications 17 no 8 (2018) DOI: 10.1142/S0219498818501578 (subscription site); pdf ; arXiv ; HAL
  17. Degenerations in Triangulated Categories to appear in Oberwolfach Reports 2016-1607b pdf
  18. with Serge Bouc ; On a question of Rickard on Tensor Product of Stably Equivalent Algebras Experimental Mathematics 26 (no 1) (2017) 31-44. pdf and arxiv ; HAL DOI:10.1080/10586458.2015.1107869
  19. Batalin-Vilkovisky Algebras, Tamarkin-Tsygan Calculus and Algebras with Duality, Proceedings of the 47th Symposium on Ring Theory and Representation Theory September 13-15, 2014. Saitama University, February 2015, pp 146-153. pdf
  20. Remarks on a Categorical Definition of Degeneration in Triangulated Categories, Proceedings of the 47th Symposium on Ring Theory and Representation Theory September 13-15, 2014. Saitama University, February 2015, pp 138-145. pdf and arxiv ; HAL
  21. with Yuming Liu and Guodong Zhou ; Stable equivalences of Morita type do not preserve tensor products and trivial extensions of algebras appeared electronically January 25, 2017 DOI ; Proceedings of the American Mathematical Society 145 (no 5) (2017) 1881-1890; pdf and arxiv (old version: title changed, slight editorial modifications in pdf)
  22. with Thierry Lambre and Guodong Zhou ; The Hochschild cohomology ring of a Frobenius algebra with semisimple Nakayama automorphism is a Batalin-Vilkovisky algebra Journal of Algebra 446 (2016) 103-131. pdf and dvi and arxiv
    A correction of a mistake detected by Matthew Antrobus.
  23. with Manuel Saorin ; An axiomatic approach for degenerations in triangulated categories Applied Categorical Structures 24 (2016) no 4, 385-405; DOI 10.1007/s10485-015-9401-3 pdf and arxiv ; HAL and Springer read only share initiative
  24. The Ring of Polynomial Functors of Prime Degree Transactions of the American Mathematical Society 367 (2015) 7161-7192 pdf arXiv ; HAL
    The paper was originally written jointly with Steffen König. Unfortunately Steffen lost interest in the subject, and with mail from Friday April 12, 2013 Steffen authorised me to publish the paper alone.
  25. Representation Theory: A homological Algebra Point of View book (xx+707 pages) submitted 10 March 2013, revised 27 January 2014, accepted 8 March 2014, appeared August 2014 with Springer Verlag, Algebra and Applications Volume 19, ISBN 978-3-319-07967-7.
    See here for the homepage at Springer. See here for an errata list.
  26. with Guodong Zhou ; On singular equivalences of Morita type Journal of Algebra 385 (2013) 64-79 pdf dvi HAL
  27. A Noether-Deuring theorem for derived categories Glasgow Mathematical Journal 54 (issue 3) (2012) 647-654; arXiv ; HAL
    the version published in Glasgow Mathematical Journal pdf
    unfortunately, in May 2012 I discovered an error in the statement Theorem 1 concerning the condition on the extension of S over R. The rectified version is pdf
  28. with Thorsten Holm ; Deformed preprojective algebras of type L: Külshammer spaces and derived equivalences Journal of Algebra 346 no1 (2011) 116-146; dvi pdf arXiv HAL ;
  29. On the use of Külshammer type invariants in representation theory Bulletin of the Iranian Mathematical Society vol.37 no.2 (2011) 291-341 dvi pdf arXiv ; HAL
    The paper can be downloaded freely here.
  30. with Guodong Zhou ; Auslander-Reiten conjecture for symmetric algebras of polynomial growth ''Beiträge zur Algebra und Geometrie'' 53 (2012) 349-364 (Contributions to Algebra and Geometry) dvi pdf arXiv ; HAL DOI:10.1007/s13366-011-0036-8 springerlink online first
    A correction rectifying the consequences of an error in the paper [20].
  31. with Guodong Zhou ; Classifying tame blocks and related algebras up to stable equivalences of Morita type Journal of Pure and Applied Algebra 215 (2011) 2969-2986 dvi pdf arXiv ; HAL
  32. with Yuming Liu and Guodong Zhou ; Higman ideal, stable Hochschild homology and Auslander-Reiten conjecture Mathematische Zeitschrift 270 (2012) 759-781 dvi pdf . DOI:10.1007/s00209-010-0825-z springerlink online first
  33. Hochschild homology invariants of Külshammer type of derived categories Communications in Algebra 39 (Vol 8) (2011) 2963-2980. dvi pdf arXiv ; HAL
  34. with Wolfgang Willems ; On Morita theory for self-dual modules Quarterly Journal of Mathematics (Oxford), 40 (2009) 387-400. dvi pdf arXiv ; HAL
  35. with Thorsten Holm ; Generalized Reynolds ideals and derived equivalences for algebras of dihedral and semidihedral type Journal of Algebra 320 (2008) 3425-3437 dvi ps arXiv ; HAL
  36. with Christine Bessenrodt and Thorsten Holm ; Generalized Reynolds Ideals for Non symmetric algebras, Journal of Algebra 312 (2007) 985-994.
    now freely available by the Elsevier open access initiative. dvi pdf arXiv
  37. Fine Hochschild invariants of derived categories for symmetric algebras Journal of Algebra 308 (2007) 350-367, dvi pdf arXiv ; HAL
    See here for the published article, now freely available by the Elsevier open access initiative.
    L. Rubio y Degrassi found a gap in the proofs of Lemma 4.2 and Proposition 4.4. His joint paper with Benjamin Briggs not only fixes the gap, but also generalizes the result nicely to stable equivalences of Morita type.
  38. Invariance of generalized Reynolds ideals under derived equivalences Mathematical Proceedings of the Royal Irish Academy 107A (1), 1-9 (2007) dvi pdf arXiv ; HAL
    and the Oberwolfach report on the article (in pdf )
    In November 2008 the article was studied in the Groupe de Travail Interuniversitaire d'Algèbre par Rachel Taillefer. She kindly wrote a detailed version of the article.
  39. with Bernt Tore Jensen and Xiuping Su ; Degeneration-like order in triangulated categories Journal of Algebra and its applications 4 (2005) 587-597; dvi pdf
  40. with Bernt Tore Jensen and Xiuping Su ; Degenerations for derived categories Journal of Pure and Applied Algebra 198 (2005) 281-295.
    Now freely available by Elsevier's open access intiative. dvi pdf arXiv ; HAL
  41. Automorphisms of Green orders and their derived categories ''Algebras and Representation Theory'' 7 (1) (2004) 19-34 dvi pdf ; see here for the Journal's page, provided jour institution subscribed for the Journal.
  42. with Raphaël Rouquier ; Picard groups for derived module categories, Proceedings of the London Mathematical Society (3) 87 (2003), 197-225. dvi pdf
    See here for the abstract published by the London Mathematical Society.
  43. Comments on gentleness of endomorphism algebras , Algebra Montpellier Announcements 1-2003 ; or dvi pdf
  44. with Jan Schröer ; Stable endomorphism algebras of modules over special biserial algebras , Mathematische Zeitschrift 244 (2003) 515-530. dvi pdf arXiv
    As remarked by Guodong Zhou in his thesis , Lemma 3.1, Lemma 3.2 and Lemma 3.2 are false as stated. The Lemmas can be modified though so that the final use in the proof of the main theorem is unaltered. See the pdf-file or the correcponding See the ps-file
  45. Self-tilting complexes yield unstable modules Transactions of the American Mathematical Society 354 (2002) 2707-2724 dvi pdf
    See here for the Transactions of the AMS homepage from where you can download the article; provided your institution subscribed for the TAMS.
  46. Auto-equivalences of derived categories acting on cohomology; Archiv der Mathematik 79 (2002) 93-103 dvi pdf
  47. with Eric Jespers ; Sl2-action on the cohomology of a rank two abelian group with arbitrary coefficient domain Proceedings of the American Mathematical Society 130 (2002) 315-325 dvi pdf
    See here for the Proceedings of the AMS homepage from where you can download the article; provided your institution subscribed for the PAMS.
  48. Self-equivalences of the derived category of a Brauer tree algebra with exceptional vertices An. St. Univ. Ovidius Constantza 9 (1) (2001) 139-148
    birthday volume for Professor Mirela Stefanescu dvi pdf . In the meantime the paper appeared. You find the ps-file of the printed version with a nice university seal on the top here .
  49. Cohomology of groups and splendid equivalences of derived categories Mathematical Proceedings of the Cambridge Philosophical Society 131 (2001) 459-472 dvi pdf .
  50. Braid groups as self-equivalences of derived categories, in Roggenkamp and Stefanescu (eds), Proceedings of the NATO ASI ``Algebra-Representation Theory'', Constanta 2000; Kluwer NATO Science Series (2001), pages 419-438. dvi pdf
  51. Cohomology of Groups, Abelian Sylow subgroups and Splendid Equivalences, Algebra Montpellier Announcements 01-2000 , 5 pages.
  52. Tilted symmetric orders are symmetric orders, Archiv der Mathematik 73 (1999) pages 15-17. dvi pdf
  53. with Steffen König ; Derived equivalences for group rings, (with contributions by Bernhard Keller, Markus Linckelmann, Jeremy Rickard and Raphael Rouquier) 255 pages, Springer Lecture Notes in Mathematics 1685 (1998).
    see an errata list in dvi-format, errata list in pdf-format.
  54. Twosided tilting complexes for Gorenstein orders, Journal of Algebra 209 (1998) 585-621.
    now freely availble by Elsevier open access initiative dvi pdf
  55. Twosided tilting complexes for Green orders and Brauer tree algebras, Journal of Algebra 187 (1997), 446-473.
    now freely availble by Elsevier open access initiative dvi pdf
  56. with Steffen König ; Tilting selfinjective algebras and Gorenstein orders, Oxford Quarterly Journal of Mathematics (2) 48 (1997) 351-361. dvi pdf
  57. Derived Equivalences of Orders, in Proceedings of the ICRA VII, Mexico, eds: Bautista, Martinez, de la Pena. Can. Math. Soc. Conference Proceedings 18, (1996) 721--749. dvi pdf
  58. with Steffen König ; Tilting hereditary orders, Communications in Algebra 24 (6) (1996) 1897--1913. dvi pdf
  59. Torsion units in integral group rings, conjugacy classes locally versus globally, Archiv der Mathematik 66 No. 6 (1996) 455-466 dvi pdf
  60. with Klaus W. Roggenkamp A counterexample to the isomorphism problem for infinite polycyclic groups, Journal of Pure and Applied Algebra 103 (1995) pages 101--103.
    Now freely available by the Elsevier open access initiative. ps
  61. with Klaus W. Roggenkamp ; Outer group automorphisms may become inner in the integral group ring, Journal of Pure and Applied Algebra 103 (1995) pages 91--99.
    Now freely available by the Elsevier open access initiative. dvi pdf
  62. On the torsion units in integral group rings of dihedral 2--groups, Journal of Algebra 175 (1995), pages 122-136.
    now freely available by the Elsevier open access initiative dvi pdf
  63. Conjugacy of involutions in integral group rings of certain dihedral and semidihedral groups, Sitzungsberichte der gemeinnützigen Akademie der Wissenschaften zu Erfurt, Mathematisch Naturwissenschaftliche Klasse 4 (1993) pages 77--88. dvi pdf
  64. Involutions in integral group rings of certain dihedral groups, Comptes rendus mathématiques de l'académie des sciences de la sociéeté royale du Canada XIV no. 4 (1992), pages 148--150.
  65. with Klaus W. Roggenkamp ; On the isomorphism problem for integral group rings of finite groups, Archiv der Mathematik 59 (1992) pages 534--544.
    This result heavily depends on an unpublished manuscript by Roggenkamp and Scott cited [4,5] in the paper. The proof there contains a flaw, which is now fixed by Martin Hertweck ''Units of p-power order in principal p-blocks of p-constrained groups'', Journal of Algebra 464 (2016) 348-356.
  66. Chapter XIII Group extensions, in: Klaus W. Roggenkamp and Martin J. Taylor, Group Rings and Class Groups, Birkhäuser Verlag Basel 1992, pages 104--116.
  67. Endliche Untergruppen der Einheitengruppe ganzzahliger Gruppenringe, Dissertation (thesis) Universität Stuttgart 1992. dvi pdf

    Education, local reports

  68. Effet d'une équivalence dérivée sur une algèbre Ext. Proceedings of the Séminaire Itinérant des Catégories dvi pdf
  69. Sur les représentations des ordres et des groupes , (1998) 17 pages, in Actes des ''Journées Mathématiques-Informatique'' Vol. 7. dvi pdf
  70. Green correspondence and structure of blocks with cyclic defect groups, dans: K. W. Roggenkamp, M. Stefanescu (eds.), 'Proceedings of the Workshop in Representation theory', Constantza 1995, An. St. Univ. Ovidius Constantza, Vol. 4 (1996), f.1, pages 24--73. dvi pdf
  71. Sur les foncteurs polynomiaux (2004) 4 pages, in Actes du Séminaire itinérant des catégories dvi pdf

    unpublished manuscripts

  72. with Jae Keol Park A Note on Semihereditary Orders (1994) 10 pages, unpublished manuscript pdf
  73. with Eric Jespers ; Group automorphism Action on Group Cohomology, (2000) 13 pages, preprint dvi pdf . a note
  74. with Guodong Zhou; Verdier quotients of homotopy categories 20 pages, 11 November 2017 ; revision and extension: 28 november 2017; second revision 28 May 2018 pdf ; arXiv
    The main results Theorem 2.1 and 2.2, as well as their corollaries are rather immediate consequences of Lemma 1 in Section 2.1 of ''Jean-Louis Verdier; Des catégories dérivées des catégories abéliennes, Astérisque 239 (1996) Chapitre 2, Proposition 2.3.1.c).'' or of ''Yann Palu, Grothendieck group and generalized mutation rule for 2-Calabi-Yau triangulated categories; Journal or pure and applied Algebra 213 (2009) 1438-1449''

To Klaus Roggenkamp's sixtieth birthday

with Steffen König a laudatio dvi pdf