On a new class of non-dynamical ABCD algebras for classical and quantum integrable systems
Year: 2024
Type: article
Abstract: We consider classical and quantum non-dynamical quadratic abcd Lax algebras with classical and quantum gl(n)⊗gl(n)-valued abcd-tensors satisfying a set of quadratic non-dynamical Yang-Baxter-type equations generalizing those of Fredel and Maillet [1]. We establish a relation of some of these equations with the so-called “semi-dynamical” Yang-Baxter equations of [2]. We show that the linearization of the corresponding quadratic structures lead to linear tensor structures with the classical gl(n)⊗gl(n)-valued r-matrices satisfying usual “permuted” classical Yang-Baxter equations [1,3–5]. We consider example of our construction associated with the deformed Zn-graded r-matrix of [9–11] and explicitly construct the corresponding abcd-tensors — both classical and quantum. Small n examples are also considered in some details.
Source: Nuclear Physics B
Author: T. Skrypnyk
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4402982105