Bulletin of the Belgian Mathematical Society - Simon Stevin

Higher Order Hochschild (Co)homology of Noncommutative Algebras

Bruce R. Corrigan-Salter

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Abstract

Hochschild (co)homology and Pirashvili's higher order Hochschild (co)homology are useful tools for a variety of applications including deformations of algebras. When working with higher order Hochschild (co)homology, we can consider the (co)homology of any commutative algebra with symmetric coefficient bimodules, however traditional Hochschild (co)homology is defined for any associative algebra with not necessarily symmetric coefficient bimodules. In the present paper, we generalize higher order Hochschild (co)homology to work with associative algebras which need not be commutative and in particular, show that simplicial sets admit such a generalization if and only if they are one dimensional.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 25, Number 5 (2018), 741-754.

Dates
First available in Project Euclid: 18 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1547780433

Mathematical Reviews number (MathSciNet)
MR3901844

Zentralblatt MATH identifier
07038550

Subjects
Primary: 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.) 16S80: Deformations of rings [See also 13D10, 14D15] 18G30: Simplicial sets, simplicial objects (in a category) [See also 55U10] 55U10: Simplicial sets and complexes

Keywords
Hochschild cohomology homology higher order multimodule

Citation

Corrigan-Salter, Bruce R. Higher Order Hochschild (Co)homology of Noncommutative Algebras. Bull. Belg. Math. Soc. Simon Stevin 25 (2018), no. 5, 741--754. https://projecteuclid.org/euclid.bbms/1547780433


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