Conjugacy classes in algebraic monoids
Author:
Mohan S. Putcha
Journal:
Trans. Amer. Math. Soc. 303 (1987), 529-540
MSC:
Primary 20G99; Secondary 20M10
DOI:
https://doi.org/10.1090/S0002-9947-1987-0902783-9
MathSciNet review:
902783
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Abstract | References | Similar Articles | Additional Information
Abstract: Let be a connected linear algebraic monoid with zero and a reductive group of units
. The following theorem is established.
Theorem. There exist affine subsets of
, reductive groups
with antiautomorphisms
, surjective morphisms
, such that: (1) Every element of
is conjugate to an element of some
, and (2) Two elements
,
in
are conjugate in
if and only if there exists
such that
. As a consequence, it is shown that
is a union of its inverse submonoids.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1987-0902783-9
Article copyright:
© Copyright 1987
American Mathematical Society