Representation theory of finite semigroups, semigroup radicals and formal language theory
By Jorge Almeida, Stuart W. Margolis, Ben Steinberg, Mikhail Volkov. 2007
90 citations recorded by the source corpus.
In this paper we characterize the congruence associated to the direct sum of all irreducible representations of a finite semigroup over an arbitrary field, generalizing results of Rhodes for the field of complex numbers. Applications are given to obtain many new results, as well as easier proofs of several results in the literature, involving: triangularizability of finite semigroups; which semigroups have (split) basic semigroup algebras, two-sided semidirect product decompositions of finite monoids; unambiguous products of rational languages; products of rational languages with counter; and Cerny's conjecture for an important class of automata.
Subfields: Computational Theory and Mathematics, Molecular Biology
View Paper: https://www.semanticscholar.org/paper/23a2f77b640f3f0db521f8f52d61a426a063a123
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In Computational Theory and Mathematics
- Ben Steinberg
- John L. Rhodes
- Volodymyr Mazorchuk
- Olexandr Ganyushkin
- Mikhail Volkov
- Mark V. Lawson
- L. O. Clark
- Stuart W. Margolis
In Molecular Biology
Citations in the corpus
- On the irreducible representations of a finite semigroup (2007, background): “This paper, like [25, 26, 19, 13, 1], aims to reconcile semigroup representation theory with representation theory at large.”
- Synchronizing Automata and the Cerny Conjecture (2008, background): “Recently Almeida et al (2008) have proved the Černý conjecture for synchronizing automata with transition monoids in DS.”
- The q-theory of Finite Semigroups (2008, methodology): “They basically give semiring analogues of the results of Munn and Ponizovskĭı on semigroup algebras over fields [202,237] by embedding the semigroup algebra (over a semiring) of a finite semigroup inside an iterated triangular product of matrix algebras over the group algebras of its maximal subgro”
- Möbius functions and semigroup representation theory II: Character formulas and multiplicities (2006, methodology): “In particular, we shall try to prove most results from [11] that we need, or refer to [ 4 ], where many results that we need are proved in a less semigroup theoretic language than [11].”