Hecke symmetries associated with the polynomial algebra in 3 commuting indeterminates

TL;DR

This paper characterizes Hecke symmetries linked to polynomial algebras generated by three commuting elements, providing explicit formulas and classification based on bivectors and symmetric bilinear forms.

Contribution

It introduces a complete description of Hecke symmetries associated with 3-variable polynomial algebras, including explicit formulas and classification criteria.

Findings

Hecke symmetries are determined by bivectors and symmetric bilinear forms.

A general formula for these symmetries is provided.

Equivalence classes of these symmetries are classified.

Abstract

It is shown in the paper that each Hecke symmetry R with the R-symmetric algebra freely generated by 3 commuting elements is determined by a bivector and a symmetric bilinear form on a 3-dimensional vector space. A general formula for such Hecke symmetries is given and the equivalence classes are described.