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: 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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DOI:
https://doi.org/10.1090/S0002-9947-1987-0902783-9

Article copyright:
© Copyright 1987
American Mathematical Society