Non-split supermanifolds associated with the cotangent bundle

Autor: Onishchik, Arkady

Publikováno v: Communications in Mathematics, Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik) (December 21, 2022) cm:9613

Here, I study the problem of classification of non-split supermanifolds having as retract the split supermanifold $(M,\Omega)$, where $\Omega$ is the sheaf of holomorphic forms on a given complex manifold $M$ of dimension $> 1$. I propose a general c

Externí odkaz: http://arxiv.org/abs/2205.12308

Transitive irreducible Lie superalgebras of vector fields

Autor: Onishchik, Arkady

Publikováno v: Communications in Mathematics, Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik) (December 14, 2022) cm:10456

Let $\mathfrak{d}$ be the Lie superalgebra of superderivations of the sheaf of sections of the exterior algebra of the homogeneous vector bundle $E$ over the flag variety $G/P$, where $G$ is a simple finite-dimensional complex Lie group and $P$ its p

Externí odkaz: http://arxiv.org/abs/2204.11033

Triangular de Rham Cohomology of Compact Kahler Manifolds

Autor: Brudnyi, A., Onishchik, A.

We study the de Rham 1-cohomology H^1_{DR}(M,G) of a smooth manifold M with values in a Lie group G. By definition, this is the quotient of the set of flat connections in the trivial principle bundle $M\times G$ by the so-called gauge equivalence. We

Externí odkaz: http://arxiv.org/abs/math/0001086

Action of vectorial Lie superalgebras on some split supermanifolds

Autor: Arkady Onishchik

The "curved" super Grassmannian is the supervariety of subsupervarieties of purely odd dimension $k$ in a~supervariety of purely odd dimension $n$, unlike the "usual" super Grassmannian which is the supervariety of linear subsuperspacies of purely od

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2efc39b558750794b43641a64d5e2ba6
https://doi.org/10.46298/cm.10455

Lifting of Holomorphic Actions on Complex Supermanifolds

Autor: Arkadi L. Onishchik

Publikováno v: Lie Groups, Geometric Structures and Differential Equations — One Hundred Years after Sophus Lie, T. Morimoto, H. Sato and K. Yamaguchi, eds. (Tokyo: Mathematical Society of Japan, 2002)

We study the problem of lifting analytic actions of a Lie group $G$ to a non-split complex analytic supermanifold $(M, \mathcal{O})$ from its retract $(M, \mathcal{O}_{\mathrm{gr}})$. In the case when $G$ is compact (or complex reductive), two criter

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::92abdfa788c3e45e681642db8e648170
https://doi.org/10.2969/aspm/03710317