✦ LIBER ✦

Types of Reductive Monoids

✍ Scribed by Zhuo Li; Mohan Putcha

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 317 KB
Volume: 221
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7946

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✦ Synopsis

Let M be a reductive monoid with a reductive unit group G. Clearly there is a natural G × G action on M. The orbits are the -classes (in the sense of semigroup theory) and form a finite lattice. The general problem of finding the lattice remains open. In this paper we study a new class of reductive monoids constructed by multilined closure. We obtain a general theorem to determine the lattices of these monoids. We find that the σ -irreducible monoids of Suzuki type and Ree type belong to this new class. Using the general theorem we then list all the lattices and type maps of the σ -irreducible monoids of Suzuki type and Ree type.

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