Plactic algebras.

DOI10.1016/j.jalgebra.2003.12.004zbMath1054.16022OpenAlexW4213013616MaRDI QIDQ1429896

Ferran Cedó, Okniński, Jan

Publication date: 27 May 2004

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2003.12.004

zbMATH Keywords

prime algebrasplactic algebrassemiprimitivity

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of finite symmetric groups (20C30) Ordinary and skew polynomial rings and semigroup rings (16S36) Free semigroups, generators and relations, word problems (20M05) Semigroup rings, multiplicative semigroups of rings (20M25)

Related Items (18)

Crystal monoids \& crystal bases: rewriting systems and biautomatic structures for plactic monoids of types \(A_{n}\), \(B_{n}\), \(C_{n}\), \(D_{n}\), and \(G_{2}\) ⋮ Irreducible representations of the Chinese monoid ⋮ Gröbner-Shirshov Bases for Plactic Algebras ⋮ Irreducible representations of the plactic algebra of rank four ⋮ Super jeu de taquin and combinatorics of super tableaux of type A ⋮ Minimal spectrum and the radical of Chinese algebras. ⋮ Algebras and groups defined by permutation relations of alternating type. ⋮ Remark on the identities of the grammic monoid with three generators ⋮ Structure of Chinese algebras. ⋮ Plactic monoids: a braided approach ⋮ Plactic algebra of rank 3 ⋮ Tropical plactic algebra, the cloaktic monoid, and semigroup representations ⋮ Finite Gröbner-Shirshov bases for plactic algebras and biautomatic structures for plactic monoids. ⋮ On finite complete rewriting systems, finite derivation type, and automaticity for homogeneous monoids ⋮ Finitely presented algebras and groups defined by permutation relations. ⋮ Chinese Algebras of Rank 3 ⋮ Grammic monoids with three generators ⋮ Identities of the plactic monoid.

Cites Work

• Recognizable subsets of the two letter plactic monoid
• Crystal graphs and \(q\)-analogues of weight multiplicities for the root system \(A_ n\)
• Permutations, matrices, and generalized Young tableaux
• Longest Increasing and Decreasing Subsequences
• On contracted semigroup rings
• Observations on group rings
• NOETHERIAN SEMIGROUP ALGEBRAS
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