6 papers
Jacobson-Morozov Lemma for Algebraic Supergroups
Inna Entova-Aizenbud, Vera Serganova
Given a quasi-reductive algebraic supergroup , we use the theory of semisimplifications of symmetric monoidal categories to define a symmetric monoidal functor $Φ_x: Rep(G) \to…
Around the center
Maria Gorelik, Vladimir Hinich, Vera Serganova
The center of a semisimple Lie algebra can be described as the algebra of W-invariant functions on the dual of the Cartan subalgebra. The centers of many Lie superalgebras have a s…
Special modules over Jordan algebras
Iryna Kashuba, Vera Serganova
In this paper we study special representations of finite-dimensional Jordan algebra whose . For each Jordan algebra of this class we consider its Tits-Kantor-Koe…
Localization theorem for homological vector fields
Vera Serganova, Alexander Sherman
We present a general theorem which computes the cohomology of a homological vector field on global sections of vector bundles over smooth affine supervarieties. The hypotheses and…
On the Jucys-Murphy method and fusion procedure for the Sergeev superalgebra
Iryna Kashuba, Alexander Molev, Vera Serganova
We use the Jucys-Murphy elements to construct a complete set of primitive idempotents for the Sergeev superalgebra . We produce seminormal forms for the simple modu…
On the Grothendieck ring of a quasireductive Lie superalgebra
Maria Gorelik, Vera Serganova, Alexander Sherman
Given a Lie superalgebra and a maximal quasitoral subalgebra , we consider properties of restrictions of -modules to . This…