Higher order Hochschild (co)homology of noncommutative algebras
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Publication:668965
zbMATH Open1412.16006arXiv1608.05466MaRDI QIDQ668965
Publication date: 20 March 2019
Published in: Bulletin of the Belgian Mathematical Society - Simon Stevin (Search for Journal in Brave)
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 able to be computed for any associative algebra with not necessarily symmetric coefficient bimodules. In a previous paper, the author generalized higher order Hochschild cohomology for multimodule coefficients (which need not be symmetric). In the current paper, we continue to 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.
Full work available at URL: https://arxiv.org/abs/1608.05466
(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Deformations of associative rings (16S80) Simplicial sets and complexes in algebraic topology (55U10)
Related Items (13)
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