Riv. Mat. Univ. Parma, Vol. 5, No. 2, 2014

Jacques Helmstetter[1]

Involutions of graded central simple algebras

Pages: 273-309
Received: 12 December 2012   
Accepted: 30 July 2013
Mathematics Subject Classification (2010): 16W10, 16W50, 15A66.
Keywords: Graded central simple algebras, involutions of algebras, Clifford algebras, spinor modules.
Author address:
[1] : Institut Fourier (Mathématiques), B.P. 74, 38400 Saint-Martin d'Hères, France

Abstract: Although much attention has already been paid to graded central simple algebras and their involutions, one piece of information is not yet well known: their involutions are classified by a cyclic group of order 8. The properties of this classification, and several problems in which it is useful, are here explained. Graded modules are the natural domain of application, but modules without gradation are also dealt with. A precise example (coming from quantum mechanics) shows which progresses this theory can achieve.


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