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The Lattice of J-Classes of (J, σ)-Irreducible Monoids, II

✍ Scribed by Zhuo Li

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 209 KB
Volume: 221
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7947

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✦ Synopsis

A reductive monoid is an algebraic monoid with a reductive unit group. Generally, we have the question of finding the orbits of the unit group of a reductive monoid acting on both sides of the monoid. Putcha and Renner give a recipe to determine the orbits for -irreducible monoids according to the Dynkin diagrams. We obtain a similar recipe for the question to σ -irreducible monoids (not -irreducible) of type D 2 n . However, there is no similar answer for types A n n ≥ 4 and E 2 6 . The fixed points of any σ -irreducible monoid under σ is a finite reductive monoid. We obtain that any such finite reductive monoid is -irreducible. Then we find the orbits of these monoids under the two sided action of their unit groups.

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The Lattice of J-Classes of (J,&#xa0;σ)-Irreducible Monoids, II

✦ Synopsis

The Lattice of J-Classes of (J, σ)-Irreducible Monoids, II