Irreducible representations of the plactic algebra of rank four
| Autor: | Jan Okniński, Łukasz Kubat, Ferran Cedó |
|---|---|
| Přispěvatelé: | Mathematics, Algebra |
| Předmět: |
Monoid
Pure mathematics Algebra and Number Theory Endomorphism 010102 general mathematics Mathematics::Rings and Algebras Jacobson radical Congruence relation 01 natural sciences Subdirect product Algebra Nilpotent Irreducible representation 0103 physical sciences 010307 mathematical physics 0101 mathematics Simple module Mathematics |
| Zdroj: | Vrije Universiteit Brussel National Information Processing Institute |
| Popis: | Irreducible representations of the plactic monoid M of rank four are studied. Certain concrete families of simple modules over the plactic algebra K [ M ] over a field K are constructed. It is shown that the Jacobson radical J ( K [ M ] ) of K [ M ] is nilpotent. Moreover, the congruence ρ on M determined by J ( K [ M ] ) coincides with the intersection of the congruences determined by the primitive ideals of K [ M ] corresponding to the constructed simple modules. In particular, M / ρ is a subdirect product of the images of M in the corresponding endomorphism algebras. |
| Databáze: | OpenAIRE |
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