Abstract Embeddings of Concrete Matrix-Groups

S. B. Mulay

A chapter in Algebra, Arithmetic and Geometry with Applications, 2004, pp 639-666 from Springer

Abstract: Abstract The groups of invertible diagonal, upper-triangular and block-triangular matrices constitute a list of distinguished concrete subgroups of GL(n,k). These, together with SL(n, k), are thought of as the standard subgroups. It is proved that when k is either a finite field (of cardinality > 3) or the algebraic closure of a finite field, many of the standard subgroups have essentially unique (abstract) embeddings in GL(n, k). With some necessary restrictions the same holds in the case of an arbitrary algebraically closed field k.

Keywords: Normal Subgroup; Parabolic Subgroup; Maximal Torus; Proper Subgroup; Algebraic Closure (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1007/978-3-642-18487-1_38

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