In this paper we extend the notion of the Brauer–Clifford group to the case of an \((S,{{\mathcal {G}}},H)\)-algebra, when H is a cocommutative Hopf algebra, \({{\mathcal {G}}}\) is a Lie algebra in the symmetric monoidal category of left H-modules, and S is a commutative algebra which is an H-module algebra, a \({\mathcal G}\)-module algebra and the H-action is compatible with the \({\mathcal {G}}\)-action. This Brauer–Clifford group turns out to be an example of the Brauer group of a symmetric monoidal category.

中文翻译：

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（$$ \ varvec {S，{{\ mathcal {G}}}，H} $$ S，G，H）的Brauer-Clifford群-Azumaya代数

在本文中，我们将Brauer–Clifford群的概念扩展到\（（S，{{\ mathcal {G}}}，H）\）-代数的情况，当H是一个可交换的Hopf代数\（（ {{\ mathcal {G}}} \）是左H-模的对称单项范畴中的Lie代数，S是H-模代数的交换对数，即\（{\ mathcal G} \ -module代数，并且H -action与\（{\ mathcal {G}} \） - action兼容。这个Brauer-Clifford组证明是对称单项类别的Brauer组的一个例子。