Möbius functions and semigroup representation theory.

DOI10.1016/j.jcta.2005.08.004zbMath1148.20049OpenAlexW2044138171MaRDI QIDQ2497971

Benjamin Steinberg

Publication date: 4 August 2006

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2005.08.004

zbMATH Keywords

Möbius functionsrepresentation theorycentral idempotentsfinite semigroupsinverse semigroupssemigroup algebrasrandom walks on semigroups

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Semigroup rings, multiplicative semigroups of rings (20M25) Inverse semigroups (20M18) Representation of semigroups; actions of semigroups on sets (20M30)

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Cites Work

• Unnamed Item
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• The Bruhat decomposition, Tits system and Iwahori ring for the monoid of matrices over a finite field
• Analogue of the Bruhat decomposition for algebraic monoids
• Sur le produit de concatenation non ambigu
• Semigroups, rings, and Markov chains
• Linear algebraic monoids.
• Representations of the rook monoid.
• A combinatorial description of the spectrum for the Tsetlin library and its generalization to hyperplane arrangements
• Characters of finite semigroups
• Finite dimensional convolution algebras
• The l 1 -Algebra of a Commutative Semigroup
• Representation theory of finite semigroups, semigroup radicals and formal language theory
• On the theory of inverse semigroups and generalized groups
• A SYNTACTICAL PROOF OF LOCALITY OF DA
• Characters and complexity of finite semigroups
• Isometries Between B ∗ -Algebras
• The Burnside algebra of a finite group