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ON SUBGROUPS OF CLIFFORD GROUPS DEFINED BY JORDAN PAIRS OF RECTANGULAR MATRICES

Part of: Jordan algebras

Published online by Cambridge University Press:  21 October 2010

HISATOSHI IKAI
HISATOSHI IKAI*
Affiliation:
Aramaki-aza-aoba 400-A-101, Sendai 980-0845, Japan (email: [email protected])
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Abstract

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Some embeddings of general linear groups into hyperbolic Clifford groups are constructed generically by using Jordan pairs of rectangular and alternating matrices over a ring. In low rank cases through exceptional isomorphisms, their direct description and relationships to some automorphisms of Clifford groups are given. Generic norms are calculated in detail, and equivariant embeddings of representation spaces are constructed.

Keywords

Clifford groupsJordan pairsgroup schemes

MSC classification

Secondary: 17C30: Associated groups, automorphisms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 89 , Issue 2 , October 2010 , pp. 215 - 232
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

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