Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics

• URL: http://arxiv.org/abs/2402.11952v1
• Date: Mon, 19 Feb 2024 08:47:06 GMT
• Title: Orthosymplectic $Z_2\times Z_2$-graded Lie superalgebras and parastatistics
• Authors: N.I. Stoilova and J. Van der Jeugt
• Abstract summary: $g$ is a $Ztimes Z$-graded algebra with a bracket $[.,.]$ that satisfies certain graded versions of the symmetry and Jacobi identity. We construct the most general orthosymplectic $Ztimes Z$-graded Lie superalgebra $osp (2m+1,2m|2n_1,2n_2)$. Some special cases are of particular interest, even when one is dealing with parabosons only.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A $Z_2\times Z_2$-graded Lie superalgebra $g$ is a $Z_2\times Z_2$-graded algebra with a bracket $[.,.]$ that satisfies certain graded versions of the symmetry and Jacobi identity. In particular, despite the common terminology, $g$ is not a Lie superalgebra. We construct the most general orthosymplectic $Z_2\times Z_2$-graded Lie superalgebra $osp(2m_1+1,2m_2|2n_1,2n_2)$ in terms of defining matrices. A special case of this algebra appeared already in work of Tolstoy in 2014. Our construction is based on the notion of graded supertranspose for a $Z_2\times Z_2$-graded matrix. Since the orthosymplectic Lie superalgebra $osp(2m+1|2n)$ is closely related to the definition of parabosons, parafermions and mixed parastatistics, we investigate here the new parastatistics relations following from $osp(2m_1+1,2m_2|2n_1,2n_2)$. Some special cases are of particular interest, even when one is dealing with parabosons only.

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