Irreducible holonomy algebras of Riemannian supermanifolds

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Authors	GALAEV Anton
Year of publication	2012
Type	Article in Periodical
Magazine / Source	Annals of Global Analysis and Geometry
MU Faculty or unit	Faculty of Science
Citation
Doi	http://dx.doi.org/10.1007/s10455-011-9299-4
Field	General mathematics
Keywords	Riemannian supermanifold; Levi-Civita superconnection; Holonomy algebra; Berger superalgebra
Description	Possible irreducible holonomy algebras g \subset osp(p,q\|2m) of Riemannian supermanifolds under the assumption that g is a direct sum of simple Lie superalgebras of classical type and possibly of a 1-dimensional center are classified. This generalizes the classical result of Marcel Berger about the classification of irreducible holonomy algebras of pseudo-Riemannian manifolds.
Related projects:	Mathematical structures and their physical applications Holonomy of Riemannian supermanifolds and related geometric structures