Generalized <i>P</i>(<i>N</i>)-graded Lie superalgebras

doi:10.1007/s11464-021-0888-7

Front. Math. China

2021, Vol. 16

Issue (3) : 647-687 https://doi.org/10.1007/s11464-021-0888-7

RESEARCH ARTICLE

Generalized P(N)-graded Lie superalgebras

Jin CHENG¹, Yun GAO²(

)

¹. School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China
². Department of Mathematics and Statistics, York University, Toronto, ON M3J 1P3, Canada

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Abstract

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.

Keywords Root system graded Lie superalgebras associative superalgebra quantum tori representations

Corresponding Author(s): Yun GAO

Issue Date: 14 July 2021

Cite this article:

Jin CHENG,Yun GAO. Generalized P(N)-graded Lie superalgebras[J]. Front. Math. China, 2021, 16(3): 647-687.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-021-0888-7
https://academic.hep.com.cn/fmc/EN/Y2021/V16/I3/647

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