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december 2018 Higher Order Hochschild (Co)homology of Noncommutative Algebras
Bruce R. Corrigan-Salter
Bull. Belg. Math. Soc. Simon Stevin 25(5): 741-754 (december 2018). DOI: 10.36045/bbms/1547780433

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.

Citation

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Bruce R. Corrigan-Salter. "Higher Order Hochschild (Co)homology of Noncommutative Algebras." Bull. Belg. Math. Soc. Simon Stevin 25 (5) 741 - 754, december 2018. https://doi.org/10.36045/bbms/1547780433

Information

Published: december 2018
First available in Project Euclid: 18 January 2019

zbMATH: 07038550
MathSciNet: MR3901844
Digital Object Identifier: 10.36045/bbms/1547780433

Subjects:
Primary: 16E40, 16S80, 18G30, 55U10

Rights: Copyright © 2018 The Belgian Mathematical Society

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Vol.25 • No. 5 • december 2018
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