Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 
 

 

Hochschild homology and trivial extension algebras


Authors: Petter Andreas Bergh and Dag Oskar Madsen
Journal: Proc. Amer. Math. Soc. 145 (2017), 1475-1480
MSC (2010): Primary 16E40, 16S70
DOI: https://doi.org/10.1090/proc/13363
Published electronically: October 20, 2016
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that if an algebra is either selfinjective, local or graded, then the Hochschild homology dimension of its trivial extension is infinite.


References [Enhancements On Off] (What's this?)

  • [AvI] Luchezar L. Avramov and Srikanth Iyengar, Gaps in Hochschild cohomology imply smoothness for commutative algebras, Math. Res. Lett. 12 (2005), no. 5-6, 789-804. MR 2189239, https://doi.org/10.4310/MRL.2005.v12.n6.a1
  • [AV-P] Luchezar L. Avramov and Micheline Vigué-Poirrier, Hochschild homology criteria for smoothness, Internat. Math. Res. Notices 1 (1992), 17-25. MR 1149001, https://doi.org/10.1155/S1073792892000035
  • [BBFS] Th. Belzner, W. D. Burgess, K. R. Fuller, and R. Schulz, Examples of ungradable algebras, Proc. Amer. Math. Soc. 114 (1992), no. 1, 1-4. MR 1062382, https://doi.org/10.2307/2159775
  • [BHM] Petter Andreas Bergh, Yang Han, and Dag Madsen, Hochschild homology and truncated cycles, Proc. Amer. Math. Soc. 140 (2012), no. 4, 1133-1139. MR 2869099, https://doi.org/10.1090/S0002-9939-2011-10942-0
  • [BM1] Petter Andreas Bergh and Dag Madsen, Hochschild homology and global dimension, Bull. Lond. Math. Soc. 41 (2009), no. 3, 473-482. MR 2506831, https://doi.org/10.1112/blms/bdp018
  • [BM2] Petter Andreas Bergh and Dag Madsen, Hochschild homology and split pairs, Bull. Sci. Math. 134 (2010), no. 7, 665-676. MR 2725172, https://doi.org/10.1016/j.bulsci.2010.07.003
  • [BGMS] Ragnar-Olaf Buchweitz, Edward L. Green, Dag Madsen, and Øyvind Solberg, Finite Hochschild cohomology without finite global dimension, Math. Res. Lett. 12 (2005), no. 5-6, 805-816. MR 2189240, https://doi.org/10.4310/MRL.2005.v12.n6.a2
  • [FeP] Elsa A. Fernández and María Inés Platzeck, Presentations of trivial extensions of finite dimensional algebras and a theorem of Sheila Brenner, J. Algebra 249 (2002), no. 2, 326-344. MR 1901162, https://doi.org/10.1006/jabr.2001.9056
  • [Han] Yang Han, Hochschild (co)homology dimension, J. London Math. Soc. (2) 73 (2006), no. 3, 657-668. MR 2241972, https://doi.org/10.1112/S002461070602299X
  • [Hap] Dieter Happel, Hochschild cohomology of finite-dimensional algebras, Séminaire d'Algèbre Paul Dubreil et Marie-Paul Malliavin, 39ème Année (Paris, 1987/1988) Lecture Notes in Math., vol. 1404, Springer, Berlin, 1989, pp. 108-126. MR 1035222, https://doi.org/10.1007/BFb0084073
  • [SV-P] Andrea Solotar and Micheline Vigué-Poirrier, Two classes of algebras with infinite Hochschild homology, Proc. Amer. Math. Soc. 138 (2010), no. 3, 861-869. MR 2566552, https://doi.org/10.1090/S0002-9939-09-10168-5

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 16E40, 16S70

Retrieve articles in all journals with MSC (2010): 16E40, 16S70


Additional Information

Petter Andreas Bergh
Affiliation: Department of Mathematical Sciences, NTNU, NO-7491 Trondheim, Norway
Email: bergh@math.ntnu.no

Dag Oskar Madsen
Affiliation: Faculty of Professional Studies, Nord University, NO-8049 Bodø, Norway
Email: dag.o.madsen@nord.no

DOI: https://doi.org/10.1090/proc/13363
Keywords: Hochschild homology, trivial extensions
Received by editor(s): October 12, 2015
Received by editor(s) in revised form: June 16, 2016
Published electronically: October 20, 2016
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2016 American Mathematical Society

American Mathematical Society