$\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie (super)algebras and generalized quantum statistics
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| Formato: | Preprint |
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2025
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| _version_ | 1866917903337521152 |
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| author | Stoilova, N. I. Van der Jeugt, J. |
| author_facet | Stoilova, N. I. Van der Jeugt, J. |
| contents | We present systems of parabosons and parafermions in the context of Lie algebras, Lie superalgebras, $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie algebras and $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie superalgebras. For certain relevant $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie algebras and $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie superalgebras, some structure theory in terms of roots and root vectors is developed. The short root vectors of these algebras are identified with parastatistics operators. For the $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie algebra $so_q(2n+1)$, a system consisting of two ensembles of parafermions satisfying relative paraboson relations are introduced. For the $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie superalgebra $osp(1,0|2n_1,2n_2)$, a system consisting of two ensembles of parabosons satisfying relative parafermion relations are introduced. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie (super)algebras and generalized quantum statistics Stoilova, N. I. Van der Jeugt, J. Mathematical Physics High Energy Physics - Theory Quantum Physics We present systems of parabosons and parafermions in the context of Lie algebras, Lie superalgebras, $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie algebras and $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie superalgebras. For certain relevant $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie algebras and $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie superalgebras, some structure theory in terms of roots and root vectors is developed. The short root vectors of these algebras are identified with parastatistics operators. For the $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie algebra $so_q(2n+1)$, a system consisting of two ensembles of parafermions satisfying relative paraboson relations are introduced. For the $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie superalgebra $osp(1,0|2n_1,2n_2)$, a system consisting of two ensembles of parabosons satisfying relative parafermion relations are introduced. |
| title | $\mathbf{{\mathbb Z}_2\ \times {\mathbb Z}_2}$-graded Lie (super)algebras and generalized quantum statistics |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2501.15541 |