Generators and relations for Lie superalgebras of Cartan type
2019 (engelsk)Inngår i: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 52, nr 5, artikkel-id 055203Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]
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.
sted, utgiver, år, opplag, sider
IOP Publishing , 2019. Vol. 52, nr 5, artikkel-id 055203
Emneord [en]
Lie algebras, superalgebras, generators and relations, supergravity
HSV kategori
Identifikatorer
URN: urn:nbn:se:oru:diva-111157DOI: 10.1088/1751-8121/aae5eaISI: 000455846600003Scopus ID: 2-s2.0-85061450508OAI: oai:DiVA.org:oru-111157DiVA, id: diva2:1832117
Forskningsfinansiär
Swedish Research Council, 2015-04268
Merknad
P would like to thank Axel Kleinschmidt for valuable discussions, and the CERN theory division for providing a stimulating environment. MC and JP would like to thank Rutgers University for their hospitality, and LC and JP would like to thank the Institut des Hautes Etudes Scientifiques (IHES) for its generous support. The work of MC and JP is supported by the Swedish Research Council, project no. 2015-04268. The work of LC is supported by Simons Foundation Collaboration Grant, no. 422182. Part of the work of JP was done at the Mitchell Institute for Fundamental Physics and Astronomy at Texas A&M University, and supported in part by NSF grant PHY-1214344.
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