Editing Clifford module (section)

In [[mathematics]], a '''Clifford module''' is a [[representation of an algebra|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 algebra|abstract theory]] of Clifford modules was founded by a paper of [[Michael Atiyah|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 {{nowrap|''p'' − ''q'' (mod 8)}}. This is an algebraic form of [[Bott periodicity]].