{"title":"Orthosymplectic Z2 x Z2-graded Lie superalgebras and parastatistics","authors":"N. I. Stoilova, J. Van der Jeugt","doi":"10.1088/1751-8121/ad2726","DOIUrl":null,"url":null,"abstract":"\n A Z2 x Z2-graded Lie superalgebra g is a Z2 x Z2-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 Z2 x Z2-graded Lie superalgebra osp(2m1+1, 2m2|2n1, 2n2) 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 Z2 x Z2-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(2m1+1, 2m2|2n1, 2n2). Some special cases are of particular interest, even when one is dealing with parabosons only.","PeriodicalId":502730,"journal":{"name":"Journal of Physics A: Mathematical and Theoretical","volume":"33 12","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Physics A: Mathematical and Theoretical","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/1751-8121/ad2726","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A Z2 x Z2-graded Lie superalgebra g is a Z2 x Z2-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 Z2 x Z2-graded Lie superalgebra osp(2m1+1, 2m2|2n1, 2n2) 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 Z2 x Z2-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(2m1+1, 2m2|2n1, 2n2). Some special cases are of particular interest, even when one is dealing with parabosons only.