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| Titel: |
The group of units of a connected algebraic monoid |
| Auteur: |
Putcha, Mohan S. |
| Verschenen in: |
Linear & multilinear algebra |
| Paginering: | Jaargang 12 (1982) nr. 1 pagina's 37-50 |
| Jaar: |
1982-07 |
| Inhoud: |
Let S be a connected algebraic monoid with zero and let G denote the group of units of S. In this paper we present some evidence to support the claim that the semigroup S\G can be studied to shed some light on the structure of the algebraic group G. Let T denote a maximal torus of G and let 0=ek<c<e0=1 be a maximal chain in E(T¯). For i=1,…,k, let αi denote the number of idempotents of the [image omitted] -class of ei in ei-1T¯. Let W(G) denote the Weyl group of G. Theorem 1 ∣W(G)∣=α1…αk. Theorem 2. The following conditions are equivalent. (1) G is solvable. (2) ∣E(T¯)∩J∣≤1 for each [image omitted] -class J of S. (3) S is a semilattice of archimedean semigroups. (4) For all e,fεE(S) any eigenvalue of ef is either 0 or 1. In particular if E(S) is finite or if S is an orthodox semigroup, then G is solvable. Many other generalizations and related results are also obtained. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
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