相关论文: Differential operators on supercircle: conformally…

This paper is the next step of an ambitious program to develop conformally equivariant quantization on supermanifolds. This problem was considered so far in (super)dimensions 1 and 1|1. We will show that the case of several odd variables is…

Let K be the Lie superalgebra of contact vector fields on the supersymmetric line. We compute the action of K on the modules of differential and pseudodifferential operators between spaces of tensor densities, in terms of their conformal…

The spaces of higher-order differential operators (in Dimension 1|2), which are modules over the stringy Lie superalgebra K(2), are isomorphic to the corresponding spaces of symbols as orthosymplectic modules in non resonant cases. Such an…

Over the $(1,n)$-dimensional real supercircle, we consider the $\mathcal{K}(n)$-modules of linear differential operators, $\frak{D}^n_{\lambda,\mu}$, acting on the superspaces of weighted densities, where $\mathcal{K}(n)$ is the Lie…

Following Feigin and Fuchs, we compute the first cohomology of the Lie superalgebra $\mathcal{K}(1)$ of contact vector fields on the (1,1)-dimensional real superspace with coefficients in the superspace of linear differential operators…

We study non-trivial deformations of the natural action of the Lie superalgebra $mathcalK(1)$ of contact vector fields on the (1,1)-dimensional superspace $mathbbR^{1|1}$ of th espace of symbols. We calculate obstructions for integrability…

Let $\frak F_{\l}$ be the space of tensor densities of degree $\lambda$ on the supercircle $S^{1|1}$. We consider the space $\mathfrak{D}_{\lambda,\mu}^k$ of k-th order linear differential operators from $\frak F_{\l}$ to $\frak F_{\mu}$ as…

We compute the first cohomology spaces $H^1(\mathfrak{osp}(1|2);\mathfrak{D}_{\lambda,\mu})$ ($\lambda, \mu\in\mathbb{R}$) of the Lie superalgebra $\mathfrak{osp}(1|2)$ with coefficients in the superspace $\mathfrak{D}_{\lambda,\mu}$ of…

Over the $(1,n)$-dimensional real superspace, $n>1$, we classify $\mathcal{K}(n)$-invariant binary differential operators acting on the superspaces of weighted densities, where $\mathcal{K}(n)$ is the Lie superalgebra of contact vector…

The space of m-ary differential operators acting on weighted densities is a (m+1)-parameter family of modules over the Lie algebra of vector fields. For almost all the parameters, we construct a canonical isomorphism between this space and…

We classify nontrivial deformations of the standard embedding of the Lie superalgebra K(1) of contact vector fields on the (1,1)-dimensional supercircle into the Lie superalgebra of superpseudodifferential operators on the supercircle. This…

We compute the first cohomology of the ortosymplectic Lie superalgebra $\mathfrak{osp}(1|2)$ on the (1,1)-dimensional real superspace with coefficients in the superspace $\frak{D}_{\lambda,\nu;\mu}$ of bilinear differential operators acting…

We classify anti-involutions of Lie superalgebra $\hsd$ preserving the principal gradation, where $\hsd$ is the central extension of the Lie superalgebra of differential operators on the super circle $S^{1|1}$. We clarify the relations…

We investigate the first cohomology space associated with the embedding of the Lie superalgebra $\cK(2)$ of contact vector fields on the (1,2)-dimensional supercircle $S^{1\mid 2}$ in the Lie superalgebra $\cS\Psi \cD \cO(S^{1\mid 2})$ of…

We consider the space of differential operators $\mathcal{D}_{\lambda\mu}$ acting between $\lambda$- and $\mu$-densities defined on $S^{1|2}$ endowed with its standard contact structure. This contact structure allows one to define a…

The Bol operators are unary differential operators between spaces of weighted densities on the 1-dimensional manifold invariant under projective transformations of the manifold. On the $1|n$-dimensional supermanifold (superstring)…

We entirely compute the cohomology for a natural and large class of $\mathfrak{osp}(1|2)$ modules $M$. We study the restriction to the $\mathfrak{sl}(2)$ cohomology of $M$ and apply our results to the module $M={\mathfrak D}_{\lambda,\mu}$…

We compute the first differential cohomology of the orthosymplectic Lie superalgebra $\mathfrak{osp}(2|2)$ with coefficients in the superspace of linear differential operators acting on the space of weighted densities on the…

We investigate the second cohomology space of the Lie superalgebra $\mathcal{K}(2)$ with coefficients in the superspace of weighted densities on the (1,2)-dimentional real superspace. We explicitly give cocycles spanning this cohomology…

This is a brief overview of my work on the realization of contact superconformal algebras in terms of pseudodifferential symbols on a supercircle. Also the 2-cocycles on K'(4) are given for this realization.