A note on cohomology of Clifford algebras

Bikram Banerjee; Goutam Mukherjee

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arXiv · 2202.09065

A note on cohomology of Clifford algebras

Bikram Banerjee·Goutam Mukherjee

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Abstract

In this article we construct a cochain complex of a complex Clifford algebra with coefficients in itself in a combinatorial fashion and we call the corresponding cohomology by {\it Clifford cohomology.} We show that {\it Clifford cohomology} controls the deformation of a complex Clifford algebra and can classify them up to Morita equivalence. We also study Hochschild cohomology groups and formal deformations of the algebra of smooth sections of a complex Clifford algebra bundle over an even dimensional orientable Riemannian manifold $M$ which admits a $Spin^{c}$ structure.

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Bikram Banerjee, Goutam Mukherjee. 2022-02-18. A note on cohomology of Clifford algebras. https://arxiv.org/abs/2202.09065

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