Hecke algebras and semisimplicity of monoid algebras

DOI10.1006/JABR.1999.7868zbMath0938.20053OpenAlexW2087165859MaRDI QIDQ1306899

Putcha, Mohan S.

Publication date: 20 December 1999

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.1999.7868

zbMATH Keywords

Hecke algebrasinduced charactersunit groupsBorel subgroupssemisimplicityfinite regular monoidscomplex monoid algebrasfinite Lie-type monoidssimply connected Chevalley groups

Mathematics Subject Classification ID

Hecke algebras and their representations (20C08) Linear algebraic groups over arbitrary fields (20G15) Semigroups of transformations, relations, partitions, etc. (20M20) Ordinary and skew polynomial rings and semigroup rings (16S36) Representations of associative Artinian rings (16G10) Semigroup rings, multiplicative semigroups of rings (20M25) Simple and semisimple modules, primitive rings and ideals in associative algebras (16D60) Representation of semigroups; actions of semigroups on sets (20M30)

Related Items (3)

R-POLYNOMIALS OF FINITE MONOIDS OF LIE TYPE ⋮ Idempotent conjugacy in monoids ⋮ Character theory of monoids over an arbitrary field.

Cites Work

• The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field
• Representations of Coxeter groups and Hecke algebras
• Classification of monoids of Lie type
• Monoids on groups with BN-pairs
• Complex Representations of Finite Monoids
• Complex Representations of Matrix Semigroups
• Semigroup Algebras of the Full Matrix Semigroup Over a Finite Field
• Observations on group rings
• Sandwich Matrices, Solomon Algebras, and Kazhdan-Lusztig Polynomials
• Monoid Hecke algebras
• The Canonical Compactification of a Finite Group of Lie Type
• Representations of monoids arising from finite groups of Lie type
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