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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Elsevier
2025-08-01
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| Series: | Nuclear Physics B |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321325001452 |
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| author | T. Skrypnyk |
| author_facet | T. Skrypnyk |
| author_sort | T. Skrypnyk |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-44fa3b7b70084a40a8782d4ed0fbc930 |
| institution | OA Journals |
| issn | 0550-3213 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj-art-44fa3b7b70084a40a8782d4ed0fbc9302025-08-20T02:27:10ZengElsevierNuclear Physics B0550-32132025-08-01101711693610.1016/j.nuclphysb.2025.116936On new rational non-dynamical ABCD matrices for quadratic classical and quantum algebrasT. Skrypnyk0School of Mathematics of the University of Leeds, Woodhouse, Leeds, LS2 9JT, UK; Bogolyubov Institute for Theoretical Physics, Metrologichna st.14-b, 03143, Kiev, Ukraine; Correspondence to: School of Mathematics of the University of Leeds, Woodhouse, Leeds, LS2 9JT, UK.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.http://www.sciencedirect.com/science/article/pii/S0550321325001452Lax representationQuadratic Poisson bracketsReflection-equation algebras |
| spellingShingle | T. Skrypnyk On new rational non-dynamical ABCD matrices for quadratic classical and quantum algebras Nuclear Physics B Lax representation Quadratic Poisson brackets Reflection-equation algebras |
| title | On new rational non-dynamical ABCD matrices for quadratic classical and quantum algebras |
| title_full | On new rational non-dynamical ABCD matrices for quadratic classical and quantum algebras |
| title_fullStr | On new rational non-dynamical ABCD matrices for quadratic classical and quantum algebras |
| title_full_unstemmed | On new rational non-dynamical ABCD matrices for quadratic classical and quantum algebras |
| title_short | On new rational non-dynamical ABCD matrices for quadratic classical and quantum algebras |
| title_sort | on new rational non dynamical abcd matrices for quadratic classical and quantum algebras |
| topic | Lax representation Quadratic Poisson brackets Reflection-equation algebras |
| url | http://www.sciencedirect.com/science/article/pii/S0550321325001452 |
| work_keys_str_mv | AT tskrypnyk onnewrationalnondynamicalabcdmatricesforquadraticclassicalandquantumalgebras |