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ON THE HOCHSCHILD HOMOLOGY OF INVOLUTIVE ALGEBRAS

  • RAMSÈS FERNÀNDEZ-VALÈNCIA (a1) and JEFFREY GIANSIRACUSA (a1)

Abstract

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.

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References

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1. Braun, C., Involutive A-infinity algebras and dihedral cohomology, J. Homotopy Relat. Struct. 9 (2) (2014), 317337.
2. Costello, K., Topological conformal field theories and Calabi-Yau categories, Adv. Math. 210 (1) (2007), 165214.
3. Fernàndez-València, R., On the structure of unoriented topological conformal field theories, arXiv:1503.02465, submitted.
4. Loday, J.-L. and Vallette, B., Algebraic operads, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 346 (Springer, Heidelberg, 2012).
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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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