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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
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Abstract

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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.

Information

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

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