Doubly $\kappa$-deformed Yang models, Born-selfdual $\kappa$-deformed quantum phase spaces and two generalizations of Yang models
| Autor: | Lukierski, Jerzy, Pachoł, Anna |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | PoS(CORFU2023)247 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.22323/1.463.0247 |
| Popis: | Recently it was shown that by using two different realizations of $\hat{o}(1,4)$ Lie algebra one can describe one-parameter standard Snyder model and two-parameter $\kappa$-deformed Snyder model. In this paper, by using the generalized Born duality and Jacobi identities we obtain from the $\kappa$-deformed Snyder model the doubly $\kappa$-deformed Yang model which provides the new class of quantum relativistic phase spaces. These phase spaces contain as subalgebras the $\kappa$-deformed Minkowski space-time as well as quantum $\tilde{\kappa}$-deformed fourmomenta and are depending on five independent parameters. Such a large class of quantum phase spaces can be described in $D=4$ by particular realizations of $\hat{o}(1,5)$ algebra, what illustrates the property that in noncommutative geometry different $D=4$ physical models may be described by various realizations of the same algebraic structure. Finally, in the last Section we propose two new ways of generalizing Yang models: by introducing $\hat o(1,3+2N)$ algebras ($N=1,2\ldots$) we provide internal symmetries $O(N)$ symmetries in Kaluza-Klein extended Yang model, and by replacing the classical $\hat{o}(1,5)$ algebras which describe the algebraic structure of Yang models by $\hat o(1,5)$ quantum groups with suitably chosen nonprimitive coproducts. Comment: 15 pages, Contribution to PoS Corfu 2023 |
| Databáze: | arXiv |
| Externí odkaz: |
|