Involutions on rectangular Jordan pairs

被引:1
作者
McCrimmon, K [1 ]
机构
[1] Univ Virginia, Dept Math, Charlottesville, VA 22903 USA
关键词
D O I
10.1006/jabr.1999.8166
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Jordan triple systems are equivalent to Jordan pairs with involution. In recent work with D'Amour on triples of Clifford type we described involutions on pairs M-1,M-q(Delta). Generalizing these results, in this paper we describe all involutions on nondegenerate pairs of rectangular type A(R,M,f)(J) having a simple artinian coordinate algebra R or, more generally, a simple unital coordinate algebra such that the form f is unital valued: f(u,v) = 1 for some u is an element of M+, v is an element of M-. The involutions are of "hermitian" type determined by an involution (anti-automorphism cr with sigma(2) = 1) on the coordinate ring, "automorphism" type determined by an automorphism sigma on the coordinate ring with sigma(2) inner, or of "isomorphism" type determined by an isomorphism sigma of the (necessarily non-artinian) coordinate ring onto a proper subring (with sigma(2) somewhat inner). (C) 2000 Academic Press.
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页码:885 / 903
页数:19
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