Party-Hecke algebras
Diego Arcis, Jes\'us Juyumaya

TL;DR
Party-Hecke algebras are a new two-parameter deformation of party algebras, constructed via basis and quotient methods, linking to braid and tie algebra structures.
Contribution
Introduces the novel concept of Party-Hecke algebras, expanding the algebraic framework with a basis construction and connections to braid and tie algebraic structures.
Findings
Defined a basis for Party-Hecke algebras
Realized these algebras as quotients of braid and tie algebras
Explored relationships between party monoid and tied symmetric monoid
Abstract
Party-Hecke algebras are introduced as a two-parameter deformation of party algebras, where one parameter deforms the party generators and the other deforms the elementary transpositions. We construct a basis for this algebra and show that it can be realized as a quotient of the algebra of braids and ties. Furthermore, we study the party monoid and its relationship with the tied symmetric monoid and their associated algebras.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic structures and combinatorial models · semigroups and automata theory
