Frontiers of Mathematics in China >
Generalized P(N)-graded Lie superalgebras
Received date: 16 Nov 2020
Accepted date: 17 Dec 2020
Published date: 15 Jun 2021
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We generalize the P(N)-graded Lie superalgebras of Martinez-Zelmanov. This generalization is not so restrictive but suffcient enough so that we are able to have a classification for this generalized P(N)-graded Lie superalgebras. Our result is that the generalized P(N)-graded Lie super-algebra L is centrally isogenous to a matrix Lie superalgebra coordinated by an associative superalgebra with a super-involution. Moreover, L is P(N)-graded if and only if the coordinate algebra R is commutative and the super-involution is trivial. This recovers Martinez-Zelmanov's theorem for type P(N). We also obtain a generalization of Kac's coordinatization via Tits-Kantor-Koecher construction. Actually, the motivation of this generalization comes from the Fermionic-Bosonic module construction.
Jin CHENG , Yun GAO . Generalized P(N)-graded Lie superalgebras[J]. Frontiers of Mathematics in China, 2021 , 16(3) : 647 -687 . DOI: 10.1007/s11464-021-0888-7
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