Cohomology rings of the plactic monoid algebra via a Gröbner–Shirshov basis

DOI10.1142/S0219498816500821zbMath1355.16006arXiv1411.5464MaRDI QIDQ2801828

Viktor Lopatkin

Publication date: 22 April 2016

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.5464

zbMATH Keywords

plactic monoidGröbner-Shirshov basisalgebraic discrete Morse theoryAnick's resolution

Mathematics Subject Classification ID

(Co)homology of rings and associative algebras (e.g., Hochschild, cyclic, dihedral, etc.) (16E40) Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting) (16S15) Free semigroups, generators and relations, word problems (20M05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Syzygies, resolutions, complexes and commutative rings (13D02)

Related Items (5)

Gröbner-Shirshov basis and Hochschild cohomology of the group \(\Gamma^4_5\) ⋮ Finite convergent presentation of plactic monoid for type C ⋮ Plactic monoids: a braided approach ⋮ Anick complex, Hochschild cohomology, Hilbert and Poincare series of the Manturov (3,4)-group ⋮ Cohomology of idempotent braidings with applications to factorizable monoids

Uses Software

• ANICK

Cites Work

• Quillen homology for operads via Gröbner bases
• Finite Gröbner-Shirshov bases for plactic algebras and biautomatic structures for plactic monoids.
• Gröbner-Shirshov bases for Lie algebras: after A. I. Shirshov
• A user's guide to discrete Morse theory
• PARASTATISTICS ALGEBRA, YOUNG TABLEAUX AND THE SUPER PLACTIC MONOID
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