Algebraic Framework for Quantization of Nonultralocal Models

TL;DR

This paper develops an algebraic framework extending braid relations to quantize nonultralocal models, providing new conditions for consistency and solutions for specific algebra classes.

Contribution

It introduces an extension of braid relations for multiple tensor products, enabling the quantization of nonultralocal models with explicit solutions for certain algebra types.

Findings

Extended braid relations for nonultralocal models

Derived Yang--Baxter--type consistency conditions

Solved equations for homogeneous and local algebras of order 2

Abstract

Extension of the braid relations to the multiple braided tensor product of algebras that can be used for quantization of nonultralocal models is presented. The Yang--Baxter--type consistency conditions as well as conditions for the existence of the multiple coproduct (monodromy matrix), which can be used for construction of the commuting subalgebra, are given. Homogeneous and local algebras are introduced, and simplification of the Yang--Baxter--type conditions for them is shown. The Yang--Baxter--type equations and multiple coproduct conditions for homogeneous and local of order 2 algebras are solved.