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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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