Cohomology Rings of Plactic Monoid Algebra via Groubner-Shirshov Basis
Viktor Lopatkin
TL;DR
This paper computes the cohomology and Hochschild cohomology rings of the plactic monoid algebra using Anick's resolution and Gröbner-Shirshov basis, providing algebraic insights into its structure.
Contribution
It introduces a method to calculate cohomology rings of plactic monoid algebra using Anick's resolution and Gröbner-Shirshov basis, which is novel in this context.
Findings
Cohomology ring of plactic monoid algebra explicitly computed
Hochschild cohomology ring determined for the algebra
Method demonstrates effectiveness of Anick's resolution with Gröbner-Shirshov basis
Abstract
In this paper we shall calculate the cohomology ring and Hochschild's cohomology ring of plactic monoid algebra via Anick's resolution using Groubner-Shirshov basis
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra