2025/01/26 by N. I. Stoilova, Stoilova, N. I., J. Van der Jeugt +1
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2501.15541
openalex publication_date 2025/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present systems of parabosons and parafermions in the context of Lie algebras, Lie superalgebras, \mathbf\mathbb Z2 × \mathbb Z2-graded Lie algebras and \mathbf\mathbb Z2 × \mathbb Z2-graded Lie superalgebras. For certain relevant \mathbf\mathbb Z2 × \mathbb Z2-graded Lie algebras and \mathbf\mathbb Z2 × \mathbb Z2-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 Z2 × \mathbb Z2-graded Lie algebra soq(2n+1), a system consisting of two ensembles of parafermions satisfying relative paraboson relations are introduced. For the \mathbf\mathbb Z2 × \mathbb Z2-graded Lie superalgebra osp(1,0|2n1,2n2), a system consisting of two ensembles of parabosons satisfying relative parafermion relations are introduced.