Work

On new rational non-dynamical ABCD matrices for quadratic classical and quantum algebras

Year: 2025

Type: article

Abstract: We consider classical and quantum non-dynamical quadratic abcd Lax algebras with rational classical and quantum gl(n)⊗gl(n)-valued abcd-tensors satisfying a set of quadratic “differential” or “semi-dynamical” [3] Yang-Baxter-type equations generalizing those of Fredel and Maillet [2]. The linearization of the corresponding quadratic structure lead to linear tensor structure with the classical gl(n)⊗gl(n)-valued non-dynamical, non-skew-symmetric rational r-matrix coinciding with a quasi-graded deformation of the standard skew-symmetric rational r-matrix [7]. The classical and quantum abcd structures corresponding to the simplest n=2 case are considered in details.

Source: Nuclear Physics B

DOI: 10.1016/j.nuclphysb.2025.116936

Author: T. Skrypnyk

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Isaac Newton Institute for Mathematical Sciences, London Mathematical Society

OpenAlex ID: W4410022682

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Cites: 20

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Related to: 10