On $Q$-deformations of Postnikov-Shapiro algebras
Anatol N. Kirillov, Gleb Nenashev
TL;DR
This paper introduces and analyzes $Q$-deformations of Postnikov-Shapiro algebras associated with graphs, providing new formulas for their dimensions and a novel 'square-free' algebra definition.
Contribution
It develops $Q$-deformations of Postnikov-Shapiro algebras, determines their total dimensions, and offers a new 'square-free' algebra construction for graphs.
Findings
Derived formulas for total dimensions of deformed algebras
Provided a new proof for dimensions of classical algebras
Constructed a 'square-free' algebra model
Abstract
For any given loopless graph , we introduce - deformations of its Postnikov-Shapiro algebras counting spanning trees, counting spanning forests and - deformations of internal algebra of . We determine the total dimension of the algebras; our proof also gives a new proof of the formula for the total dimensions of the usual Postnikov-Shapiro algebras. Furthermore, we construct "square-free" definition of usual internal algebra of .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Combinatorial Mathematics