Generalized Matsumoto-Tits sections and quantum quasi-shuffle algebras

TL;DR

This paper introduces generalized Matsumoto-Tits sections for virtual braid monoids and applies them to analyze the defining relations of quantum quasi-shuffle algebras, advancing algebraic understanding in quantum algebra.

Contribution

It defines generalized Matsumoto-Tits sections for virtual braid monoids and uses them to study quantum quasi-shuffle algebra relations.

Findings

Defined generalized Matsumoto-Tits sections for virtual braid monoids

Applied these sections to analyze quantum quasi-shuffle algebra relations

Provided new insights into the algebraic structure of quantum quasi-shuffle algebras

Abstract

In this paper generalized Matsumoto-Tits sections lifting permutations to the algebra associated to a generalized virtual braid monoid are defined. They are then applied to study the defining relations of the quantum quasi-shuffle algebras via the total symmetrization operator.