Abstract
We generalize the P(N)-graded Lie superalgebras of Martinez-Zelmanov. This generalization is not so restrictive but sufficient 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 superalgebra 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.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11701340, 11931009) and the NSERC of Canada.
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Cheng, J., Gao, Y. Generalized P(N)-graded Lie superalgebras. Front. Math. China 16, 647–687 (2021). https://doi.org/10.1007/s11464-021-0888-7
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DOI: https://doi.org/10.1007/s11464-021-0888-7