Hostname: page-component-5c6d5d7d68-tdptf Total loading time: 0 Render date: 2024-08-19T11:50:16.857Z Has data issue: false hasContentIssue false
  • English
  • Français

ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS

Published online by Cambridge University Press:  07 February 2017

RAMSÈS FERNÀNDEZ-VALÈNCIA  and
JEFFREY GIANSIRACUSA
RAMSÈS FERNÀNDEZ-VALÈNCIA
Affiliation:
Department of Mathematics, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom e-mails: ramses.fernandez.valencia@gmail.com, j.h.giansiracusa@swansea.ac.uk
JEFFREY GIANSIRACUSA
Affiliation:
Department of Mathematics, Swansea University, Singleton Park, Swansea SA2 8PP, United Kingdom e-mails: ramses.fernandez.valencia@gmail.com, j.h.giansiracusa@swansea.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We study the homological algebra of bimodules over involutive associative algebras. We show that Braun's definition of involutive Hochschild cohomology in terms of the complex of involution-preserving derivations is indeed computing a derived functor: the ℤ/2-invariants intersected with the centre. We then introduce the corresponding involutive Hochschild homology theory and describe it as the derived functor of the pushout of ℤ/2-coinvariants and abelianization.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 60 , Issue 1 , January 2018 , pp. 187 - 198
Copyright
Copyright © Glasgow Mathematical Journal Trust 2017 

References

REFERENCES

1. Braun, C., Involutive A-infinity algebras and dihedral cohomology, J. Homotopy Relat. Struct. 9 (2) (2014), 317–337.Google Scholar
2. Costello, K., Topological conformal field theories and Calabi-Yau categories, Adv. Math. 210 (1) (2007), 165–214.Google Scholar
3. Fernàndez-València, R., On the structure of unoriented topological conformal field theories, arXiv:1503.02465, submitted.Google Scholar
4. Loday, J.-L. and Vallette, B., Algebraic operads, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 346 (Springer, Heidelberg, 2012).Google Scholar