On new rational non-dynamical ABCD matrices for quadratic classical and quantum algebras
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 linearizat...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-08-01
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| Series: | Nuclear Physics B |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321325001452 |
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| Summary: | 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. |
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| ISSN: | 0550-3213 |