Party-Hecke algebras

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.