Irreducible Holonomy Algebras of Odd Riemannian Supermanifolds

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Authors	GALAEV Anton
Year of publication	2011
Type	Article in Periodical
Magazine / Source	Lobachevskii Journal of Mathematics
MU Faculty or unit	Faculty of Science
Citation
Field	General mathematics
Keywords	Riemannian supermanifold; Levi-Civita superconnection; holonomy algebra; Berger superalgebra
Description	Possible irreducible holonomy algebras g \subset sp(2m,R) of odd Riemannian supermanifolds and irreducible subalgebras g \subset gl(n,R) with non-trivial first skew-symmetric prolongations are classified. An approach to the classification of some classes of the holonomy algebras of Riemannian supermanifolds is discussed.
Related projects:	Mathematical structures and their physical applications Holonomy of Riemannian supermanifolds and related geometric structures