Monoids of Lie Type

Putcha, Mohan S.

doi:10.1007/978-94-011-0149-3_11

Cited by 4 publications

(2 citation statements)

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“…This comes from a number of sources. One is the theory of monoids of Lie type developed by Putcha, Renner and others [63,68,70,71]. These monoids can be thought of as finite analogues of linear algebraic monoids [67,76] and their representation theory gives information on their groups of units, which are groups of Lie type [69,74,75].…”

Section: Introductionmentioning

confidence: 99%

Quivers of monoids with basic algebras

Margolis

Steinberg

2012

Compositio Math.

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AbstractWe compute the quiver of any finite monoid that has a basic algebra over an algebraically closed field of characteristic zero. More generally, we reduce the computation of the quiver over a splitting field of a class of monoids that we term rectangular monoids (in the semigroup theory literature the class is known asDO) to representation-theoretic computations for group algebras of maximal subgroups. Hence in good characteristic for the maximal subgroups, this gives an essentially complete computation. Since groups are examples of rectangular monoids, we cannot hope to do better than this. For the subclass of ℛ-trivial monoids, we also provide a semigroup-theoretic description of the projective indecomposable modules and compute the Cartan matrix.

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Section: Introductionmentioning

confidence: 99%

Quivers of monoids with basic algebras

Margolis

Steinberg

2012

Compositio Math.

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“…The full linear monoid of all n × n matrices over a field (or more generally a division ring) is one of the most natural and well studied of semigroups. This monoid plays an analogous role in semigroup theory as the general linear group does in group theory, and the study of linear semigroups [28] is important in a range of areas such as the representation theory of semigroups [1], [5,Chapter 5], Putcha-Renner theory of linear algebraic monoids (monoids closed in the Zariski topology) [30,35,37], and the theory of finite monoids of Lie type [29,31,32,33].…”

Section: Introductionmentioning

confidence: 99%