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system of representations - translation to russian
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![Lie theory]]. The theory of [[manifolds]] was not discovered in Lie's time, so he worked ''locally'' with subsets of <math>\R^n.</math> The structure would today be called a '''local group'''.](https://commons.wikimedia.org/wiki/Special:FilePath/Sophus Lie.jpg?width=200 "Lie theory]]. The theory of [[manifolds]] was not discovered in Lie's time, so he worked ''locally'' with subsets of <math>\R^n.</math> The structure would today be called a '''local group'''.")
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Definition
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Wikipedia
In mathematics, a Clifford module is a representation of a Clifford algebra. In general a Clifford algebra C is a central simple algebra over some field extension L of the field K over which the quadratic form Q defining C is defined.
The abstract theory of Clifford modules was founded by a paper of M. F. Atiyah, R. Bott and Arnold S. Shapiro. A fundamental result on Clifford modules is that the Morita equivalence class of a Clifford algebra (the equivalence class of the category of Clifford modules over it) depends only on the signature p − q (mod 8). This is an algebraic form of Bott periodicity.
