Lie-Rinehart代数的Brauer-Clifford群

Pub Date : 2022-01-13 DOI:10.1142/s1005386722000086

T. Guédénon

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引用次数: 0

摘要

当[公式:见文]是交换代数且[公式:见文]是交换环上的[公式:见文]-李代数时，我们定义了[公式:见文]-Azumaya代数的Brauer-Clifford群的概念。这是在与微分几何有联系的应用中出现的情况。这个Brauer - clifford群是对称一元范畴的Brauer群的一个例子。

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Brauer–Clifford Group of Lie–Rinehart Algebras

In this paper we define the notion of Brauer–Clifford group for [Formula: see text]-Azumaya algebras when [Formula: see text] is a commutative algebra and[Formula: see text] is a [Formula: see text]-Lie algebra over a commutative ring [Formula: see text]. This is the situation that arises in applications having connections to differential geometry. This Brauer–Clifford group turns out to be an example of a Brauer group of a symmetric monoidal category.

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