Irreducible complex skew-Berger algebras

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Authors

GALAEV Anton

Year of publication 2009
Type Article in Periodical
Magazine / Source Differential Geometry and its Applications
MU Faculty or unit

Faculty of Science

Citation
Web http://dx.doi.org/10.1016/j.difgeo.2009.09.001
Field General mathematics
Keywords Holonomy algebra of a supermanifold; Berger superalgebra; Skew-Berger algebra; Skew-symmetric prolongation
Description Irreducible skew-Berger algebras $\g\subset\gl(n,\Co)$, i.e. algebras spanned by the images of the linear maps $R:\odot^2\Co^n\to\g$ satisfying the Bianchi identity, are classified. These Lie algebras can be interpreted as irreducible complex Berger superalgebras contained in $\gl(0|n,\Co)$.
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