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See detailCommutative n-ary superalgebras with an invariant skew-symmetric form
Vishnyakova, Elizaveta UL

in Journal of Geometry & Physics (2015), 98

We study nn-ary commutative superalgebras and L∞L∞-algebras that possess a skew-symmetric invariant form, using the derived bracket formalism. This class of superalgebras includes for instance Lie ... [more ▼]

We study nn-ary commutative superalgebras and L∞L∞-algebras that possess a skew-symmetric invariant form, using the derived bracket formalism. This class of superalgebras includes for instance Lie algebras and their nn-ary generalizations, commutative associative and Jordan algebras with an invariant form. We give a classification of anti-commutative mm-dimensional (m−3)(m−3)-ary algebras with an invariant form, and a classification of real simple mm-dimensional Lie (m−3)(m−3)-algebras with a positive definite invariant form up to isometry. Furthermore, we develop the Hodge Theory for L∞L∞-algebras with a symmetric invariant form, and we describe quasi-Frobenius structures on skew-symmetric nn-ary algebras. [less ▲]

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See detailOn n-ary Lie Algebras of Type (r, l)
Vishnyakova, Elizaveta UL

in Kielanowski, Piotr; Bieliavsky, Pierre; Odzijewicz, Anatol (Eds.) et al Geometric Methods in Physics (2015)

These notes are devoted to the multiple generalization of a Lie algebra introduced by A.M. Vinogradov and M.M. Vinogradov. We compare definitions of such algebras in the usual and invariant case ... [more ▼]

These notes are devoted to the multiple generalization of a Lie algebra introduced by A.M. Vinogradov and M.M. Vinogradov. We compare definitions of such algebras in the usual and invariant case. Furthermore, we show that there are no simple n-ary Lie algebras of type (n - 1, l) for l > 0. [less ▲]

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See detailOn the splitting problem for complex homogeneous supermanifolds
Vishnyakova, Elizaveta UL

in Journal of Lie Theory (2015), 25(2), 459476

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See detailOn complex analytic 1|3-dimensional supermanifolds associated with CP^1
Vishnyakova, Elizaveta UL

in Proceedings of the XXXII Workshop on Geometric Methods in Physics (2014)

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See detailSymmetric n-ary superalgebras with skew-symmetric invariant forms
Vishnyakova, Elizaveta UL

E-print/Working paper (2014)

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See detailLocally free sheaves on complex supermanifolds
Vishnyakova, Elizaveta UL

in Transformation Groups (2013), 18(2),

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See detailA classiffcation theorem and a spectral sequence for a locally free sheaf cohomology of a supermanifold
Vishnyakova, Elizaveta UL

in Geometric Methods in Physics, XXX Workshop 2011 (2013)

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See detailEven-homogeneous supermanifolds on the complex projective line.
Vishnyakova, Elizaveta UL

in Differential Geometry & its Applications (2013), 31

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