dorsal/arxiv
View SchemaCentral extensions of the families of quasi-unitary Lie algebras
| Authors | F. J. Herranz, J. C. Pérez Bueno, M. Santander |
|---|---|
| Categories | |
| ArXiv ID | physics/9801008 |
| URL | https://arxiv.org/abs/physics/9801008 |
| DOI | 10.1088/0305-4470/31/23/015 |
| Journal | J.Phys.A31:5327-5347,1998 |
Abstract
The most general possible central extensions of two whole families of Lie algebras, which can be obtained by contracting the special pseudo-unitary algebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras u(p,q), are completely determined and classified for arbitrary p,q. In addition to the su(p,q) and u({p,q}) algebras, whose second cohomology group is well known to be trivial, each family includes many non-semisimple algebras; their central extensions, which are explicitly given, can be classified into three types as far as their properties under contraction are involved. A closed expression for the dimension of the second cohomology group of any member of these families of algebras is given.
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"abstract": "The most general possible central extensions of two whole families of Lie\nalgebras, which can be obtained by contracting the special pseudo-unitary\nalgebras su(p,q) of the Cartan series A_l and the pseudo-unitary algebras\nu(p,q), are completely determined and classified for arbitrary p,q. In addition\nto the su(p,q) and u({p,q}) algebras, whose second cohomology group is well\nknown to be trivial, each family includes many non-semisimple algebras; their\ncentral extensions, which are explicitly given, can be classified into three\ntypes as far as their properties under contraction are involved. A closed\nexpression for the dimension of the second cohomology group of any member of\nthese families of algebras is given.",
"arxiv_id": "physics/9801008",
"authors": [
"F. J. Herranz",
"J. C. P\u00e9rez Bueno",
"M. Santander"
],
"categories": [
"math-ph",
"hep-th",
"math.MP",
"math.QA"
],
"doi": "10.1088/0305-4470/31/23/015",
"journal_ref": "J.Phys.A31:5327-5347,1998",
"title": "Central extensions of the families of quasi-unitary Lie algebras",
"url": "https://arxiv.org/abs/physics/9801008"
},
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