Bulletin of the Belgian Mathematical Society - Simon Stevin

Higher Order Hochschild (Co)homology of Noncommutative Algebras

Bruce R. Corrigan-Salter

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


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

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

First available in Project Euclid: 18 January 2019

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Hochschild cohomology homology higher order multimodule


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

Export citation