Homogeneous irreducible supermanifolds and graded Lie superalgebras

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F18%3A50014423" target="_blank" >RIV/62690094:18470/18:50014423 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1093/imrn/rnw262" target="_blank" >http://dx.doi.org/10.1093/imrn/rnw262</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imrn/rnw262" target="_blank" >10.1093/imrn/rnw262</a>

Result language
angličtina
Original language name
Homogeneous irreducible supermanifolds and graded Lie superalgebras
Original language description
A depth one grading g = g(-1)circle plus g(0). g(1)circle plus ...circle plus g(l) of a finite dimensional Lie superalgebra g is called nonlinear irreducible if the isotropy representation ad (g0)vertical bar(g-1) is irreducible and g(1) not equal (0). An example is the full prolongation of an irreducible linear Lie superalgebra g(0) subset of gl(g(-1)) of finite type with non-trivial first prolongation. We prove that a complex Lie superalgebra g which admits a depth one transitive nonlinear irreducible grading is a semisimple Lie superalgebra with the socle s circle times Lambda (C-n), where s is a simple Lie superalgebra, and we describe such gradings. The graded Lie superalgebra g defines an isotropy irreducible homogeneous supermanifold M = G/G(0) where G, G(0) are Lie supergroups, respectively associated with the Lie superalgebras g and g(0) := circle plus(p >= 0) g(p).
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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