Clifford algebras | Representation theory

Clifford module

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. (Wikipedia).

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Related pages

Michael Atiyah | Clifford algebra | Field extension | Quadratic form | Abstract algebra | Dirac equation | Mathematics | Weyl–Brauer matrices | Clifford module bundle | Matrix (mathematics) | Higher-dimensional gamma matrices | Central simple algebra | Morita equivalence