Zobrazeno 1 - 10
of 218
pro vyhledávání: '"SERGANOVA, VERA"'
We introduce Sylow subgroups and $0$-groups to the theory of complex algebraic supergroups, which mimic Sylow subgroups and $p$-groups in the theory of finite groups. We prove that Sylow subgroups are always $0$-groups, and show that they are unique
Externí odkaz:
http://arxiv.org/abs/2404.11077
In this paper we consider those involutions $\theta$ of a finite-dimensional Kac-Moody Lie superalgebra $\mathfrak g$, with associated decomposition $\mathfrak g=\mathfrak k\oplus\mathfrak p$, for which a Cartan subspace $\mathfrak a$ in $\mathfrak p
Externí odkaz:
http://arxiv.org/abs/2401.04652
We present a proof of a generalization of the theorem of H.~Matsumoto on Coxeter groups. Our generalized version is applicable to "graphs admitting geometric realization". The original version of the theorem for Coxeter groups is a special case when
Externí odkaz:
http://arxiv.org/abs/2310.13507
Autor:
Serganova, Vera
Publikováno v:
Journal of Algebra, Volume 258, Issue 2, 15 December 2002, Pages 615-630
We introduce a new way to study representations of the Lie superalgebra $p(n)$. Since the center of the universal enveloping algebra $U$ acts trivially on all irreducible representations, we suggest to study the quotient algebra $\bar{U}$ by the radi
Externí odkaz:
http://arxiv.org/abs/2310.12566
Autor:
Serganova, Vera
Publikováno v:
New developments in Lie Theory and its applications: Proceedings of the the seventh workshop, AMS (2011)
We call an affine algebraic supergroup quasireductive if its underlying algebraic group is reductive. We obtain some results about the structure and representations of reductive supergroups.
Comment: This is a paper from 2011. 19 pages
Comment: This is a paper from 2011. 19 pages
Externí odkaz:
http://arxiv.org/abs/2310.11820
We study the representation theory of the Lie superalgebra $\mathfrak{gl}(1|1)$, constructing two spectral sequences which eventually annihilate precisely the superdimension zero indecomposable modules in the finite-dimensional category. The pages of
Externí odkaz:
http://arxiv.org/abs/2307.06156
Autor:
Serganova, Vera, Vaintrob, Dmitry
We prove the Schwarz-Zaboronsky localization theorem for CS manifolds and use this to give a volume calculation for homogeneous superspaces for super-Lie groups that lack a real form.
Comment: 31 pages
Comment: 31 pages
Externí odkaz:
http://arxiv.org/abs/2212.07503
Autor:
Serganova, Vera, Sherman, Alexander
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 results have the clear flavor of a localization theorem.
Comment:
Comment:
Externí odkaz:
http://arxiv.org/abs/2210.13264
We introduce a notion of a root groupoid as a replacement of the notion of Weyl group for (Kac-Moody) Lie superalgebras. The objects of the root groupoid classify certain root data, the arrows are defined by generators and relations. As an abstract g
Externí odkaz:
http://arxiv.org/abs/2209.06253
Given a Lie superalgebra $\mathfrak{g}$ and a maximal quasitoral subalgebra $\mathfrak{h}$, we consider properties of restrictions of $\mathfrak{g}$-modules to $\mathfrak{h}$. This is a natural generalization of the study of characters in the case wh
Externí odkaz:
http://arxiv.org/abs/2206.07709