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Involutions on Rectangular Jordan Pairs

โœ Scribed by Kevin McCrimmon

Book ID
102576297
Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
148 KB
Volume
225
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

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 ลฝ .

M M

โŒฌ . Generalizing these results, in this paper we describe all involutions on 1, q ลฝ . J nondegenerate pairs of rectangular type A R, M, f having a simple artinian coordinate algebra R or, more generally, a simple unital coordinate algebra such ลฝ .

q y that the form f is unital-valued: f u, ยจs 1 for some u g M , ยจg M . The ลฝ involutions are of ''hermitian'' type determined by an involution anti-automor-2 . phism with s 1 on the coordinate ring, ''automorphism'' type determined by an automorphism on the coordinate ring with 2 inner, or of ''isomorphism'' ลฝ . type determined by an isomorphism of the necessarily non-artinian coordinate ลฝ 2 . ring onto a proper subring with somewhat inner .

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the number of coprime m-tuples of monic polynomials of degree n over F q is equal to q nm &q (n&1) m+1 . In particular, among the ordered pairs of polynomials of degree n over F 2 there are as many relatively prime as non-relatively prime ones. We give an involution that proves this result.