## Conjugacy classes in algebraic monoids

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- by Mohan S. Putcha PDF
- Trans. Amer. Math. Soc.
**303**(1987), 529-540 Request permission

## Abstract:

Let $M$ be a connected linear algebraic monoid with zero and a reductive group of units $G$. The following theorem is established. Theorem.*There exist affine subsets*${M_1}, \ldots ,{M_k}$

*of*$M$,

*reductive groups*${G_1}, \ldots ,{G_k}$

*with antiautomorphisms*$^{\ast }$,

*surjective morphisms*${\theta _i}:{M_i} \to {G_i}$,

*such that*: (1)

*Every element of*$M$

*is conjugate to an element of some*${M_i}$,

*and*(2)

*Two elements*$a$, $b$

*in*${M_i}$

*are conjugate in*$M$

*if and only if there exists*$x \in {G_i}$

*such that*$x{\theta _i}(a){x^{\ast }} = {\theta _i}(b)$.

*As a consequence, it is shown that*$M$

*is a union of its inverse submonoids*.

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## Additional Information

- © Copyright 1987 American Mathematical Society
- 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