13 citations · 28 across the 17 of their papers we have counts for
21 papers
Graded covering of a supermanifold
Elizaveta Vishnyakova
We introduce and investigate the notion of a -graded covering for a supermanifold. More precisely, Donagi and Witten suggested a construction of the first obstruction cl…
Automorphisms and real structures for a -symmetric super-Grassmannian
Elizaveta Vishnyakova, Mikhail Borovoi
Any complex-analytic vector bundle admits naturally defined homotheties , , i.e. is the multiplication of a local section by a complex numb…
Graded covering of a supermanifold I. The case of a Lie supergroup
Mikolaj Rotkiewicz, Elizaveta Vishnyakova
We generalize the Donagi and Witten construction of a first obstruction class for splitting of a supermanifold via differential operators using the theory of -fold vector bundle…
Rigidity of flag supermanifolds
Elizaveta Vishnyakova
We prove that under certain assumptions a supermanifold of flags is rigid, this is its complex structure does not admit any non-trivial small deformation. Moreover under the same a…
Harish-Chandra modules over invariant subalgebras in a skew-group ring
Volodymyr Mazorchuk, Elizaveta Vishnyakova
We construct a new class of algebras resembling enveloping algebras and generalizing orthogonal Gelfand-Zeitlin algebras and rational Galois algebras studied by [EMV,FuZ,RZ,Har]. T…
Vector fields on -flag supermanifolds
Elizaveta Vishnyakova
We compute the Lie superalgebras of holomorphic vector fields on isotropic flag supermanifolds of maximal type corresponding to the Lie superalgebra $\mathfrak{osp}_{2m-1|2n}(\math…