Classification of simple linearly compact n-Lie superalgebras
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Kac_Classification of (arxiv).pdf
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248.88 KB
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Author(s)
Cantarini, Nicoletta
Kac, Victor
Date Issued
April 2010
Journal
Communications in Mathematical Physics
Publisher
Springer-Verlag
Citation
Cantarini, Nicoletta, and Victor G. Kac. “Classification of Simple Linearly Compact n-Lie Superalgebras.” Communications in Mathematical Physics 298.3 (2010): 833–853. Web.
Version
Author's final manuscript
Abstract
We classify simple linearly compact n-Lie superalgebras with n > 2 over a field F of characteristic 0. The classification is based on a bijective correspondence between non-abelian n-Lie superalgebras and transitive Z-graded Lie superalgebras of the form L=n−1j=−1Lj, where dim L n−1 = 1, L −1 and L n−1 generate L, and [L j , L n−j−1] = 0 for all j, thereby reducing it to the known classification of simple linearly compact Lie superalgebras and their Z-gradings. The list consists of four examples, one of them being the n + 1-dimensional vector product n-Lie algebra, and the remaining three infinite-dimensional n-Lie algebras.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike 3.0
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DOI of Published Version
https://doi.org/10.1007/s00220-010-1049-0
