A Note on Cohomology of Clifford Algebras

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-09 DOI:10.1007/s00006-024-01324-z

Bikram Banerjee, Goutam Mukherjee

引用次数: 0

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 Clifford cohomology. We show that 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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关于克利福德代数同调的说明

在这篇文章中，我们以组合的方式构建了一个复克利福德代数的共链复数，其系数本身就是复克利福德代数，我们称相应的同调为克利福德同调。我们证明，Clifford cohomology 控制着复 Clifford 代数的变形，并能对它们进行莫里塔等价分类。我们还研究了在偶数维可定向黎曼流形 M 上的复（Clifford）代数束的光滑截面代数的霍赫希尔德（Hochschild）同调群和形式变形，该流形承认一个 \(Spin^{c}\) 结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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