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- W4252482392 abstract "In this paper we study connected regular linear algebraic monoids. If $phi :{G_0} to {text {GL}}(n,K)$ is a representation of a reductive group ${G_0}$, then the Zariski closure of $Kphi ({G_0})$ in ${mathcal {M}_n}(K)$ is a connected regular linear algebraic monoid with zero. In $S 2$ we study abstract semigroup theoretic properties of a connected regular linear algebraic monoid with zero. We show that the principal right ideals form a relatively complemented lattice, that the idempotents satisfy a certain connectedness condition, and that these monoids are $V$-regular. In $S 3$ we show that when the ideals are linearly ordered, the group of units is nearly simple of type ${A_l},{B_l},{C_l},{F_4};{text {or}};{G_2}$. In $S 4$, conjugacy classes are studied by first reducing the problem to nilpotent elements. It is shown that the number of conjugacy classes of minimal nilpotent elements is always finite." @default.
- W4252482392 created "2022-05-12" @default.
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- W4252482392 date "1985-08-01" @default.
- W4252482392 modified "2023-09-27" @default.
- W4252482392 title "Regular Linear Algebraic Monoids" @default.
- W4252482392 doi "https://doi.org/10.2307/2000302" @default.
- W4252482392 hasPublicationYear "1985" @default.
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