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   Commutative n-ary superalgebras with an invariant skew-symmetric formVishnyakova, Elizaveta  in Journal of Geometry and 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 ▲] Detailed reference viewed: 77 (4 UL)On n-ary Lie Algebras of Type (r, l)Vishnyakova, Elizaveta 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 ▲] Detailed reference viewed: 48 (0 UL) On the splitting problem for complex homogeneous supermanifoldsVishnyakova, Elizaveta in Journal of Lie Theory (2015), 25(2), 459476 Detailed reference viewed: 66 (3 UL)Symmetric n-ary superalgebras with skew-symmetric invariant formsVishnyakova, Elizaveta E-print/Working paper (2014) Detailed reference viewed: 43 (0 UL)On complex analytic 1|3-dimensional supermanifolds associated with CP^1Vishnyakova, Elizaveta in Proceedings of the XXXII Workshop on Geometric Methods in Physics (2014) Detailed reference viewed: 51 (1 UL)Locally free sheaves on complex supermanifoldsVishnyakova, Elizaveta in Transformation Groups (2013), 18(2), Detailed reference viewed: 106 (0 UL)Even-homogeneous supermanifolds on the complex projective line.Vishnyakova, Elizaveta in Differential Geometry and its Applications (2013), 31 Detailed reference viewed: 119 (3 UL)A classiffcation theorem and a spectral sequence for a locally free sheaf cohomology of a supermanifoldVishnyakova, Elizaveta in Geometric Methods in Physics, XXX Workshop 2011 (2013) Detailed reference viewed: 47 (0 UL) |
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