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Generators and rela...
Generators and relations for Lie superalgebras of Cartan type
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- Carbone, Lisa (author)
- Department of Mathematics, Rutgers University, Piscataway NJ, United States of America,Rutgers University
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- Cederwall, Martin, 1961 (author)
- Department of Physics, Chalmers University of Technology, Gothenburg, Sweden,Chalmers tekniska högskola,Chalmers University of Technology
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- Palmkvist, Jakob, 1980- (author)
- Department of Physics, Chalmers University of Technology, Gothenburg, Sweden,Chalmers tekniska högskola,Chalmers University of Technology
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(creator_code:org_t)
- 2019-01-08
- 2019
- English.
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In: Journal of Physics A. - : IOP Publishing. - 1751-8113 .- 1751-8121. ; 52:5
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Abstract
Subject headings
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- We give an analog of a Chevalley-Serre presentation for the Lie superalgebras W(n) and S(n) of Cartan type. These are part of a wider class of Lie superalgebras, the so-called tensor hierarchy algebras, denoted W(g) and S(g), where g denotes the Kac-Moody algebra A(r), D-r or E-r. Then W(A(n-1)) and S(A(n-1)) are the Lie superalgebras W(n) and S(n). The algebras W(g) and S(g) are constructed from the Dynkin diagram of the Borcherds-Kac-Moody superalgebras B(g) obtained by adding a single grey node (representing an odd null root) to the Dynkin diagram of g. We redefine the algebras W(A(r)) and S(A(r)) in terms of Chevalley generators and defining relations. We prove that all relations follow from the defining ones at level >= -2. The analogous definitions of the algebras in the D- and E-series are given. In the latter case the full set of defining relations is conjectured.
Subject headings
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Fysik -- Annan fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences -- Other Physics Topics (hsv//eng)
Keyword
- Lie algebras
- superalgebras
- generators and relations
- supergravity
Publication and Content Type
- ref (subject category)
- art (subject category)
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