Related papers: Vector fields on $\mathfrak{osp}_{2m|2n}(\mathbb C…

Let $k$ be a field with $\text{char}(k)\neq 2$. We prove that all maximal flags of composition algebras over $k$, appear as the $k$-rational $Sp_{6}$-orbits in a Zariski-dense $Sp_{6}$-invariant subset $V^{ss}\subset V=\wedge^{3}V_{6}$,…

This paper is to study vertex operator superalgebras which are strongly generated by their weight-$2$ and weight-$\frac{3}{2}$ homogeneous subspaces. Among the main results, it is proved that if such a vertex operator superalgebra $V$ is…

The purpose of this paper is presenting a theoretical basis for the study of $\omega$-Hamiltonian vector fields in a more general approach than the classical one. We introduce the concepts of $\omega$-symplectic group and…

In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…

In this paper, we address the following two general problems: given two algebraic varieties in ${\bf C}^n$, find out whether or not they are (1) isomorphic; (2) equivalent under an automorphism of ${\bf C}^n$. Although a complete solution…

There is a well-established procedure of assigning a strong homotopy Lie algebra of local observables to a multisymplectic manifold which can be regarded as part of a categorified Poisson structure. For a 2-plectic manifold, the resulting…

The theory of Lie algebras can be categorified starting from a new notion of "2-vector space", which we define as an internal category in Vect. There is a 2-category 2Vect having these 2-vector spaces as objects, "linear functors" as…

Let $\mathcal M$ be a compact complex supermanifold. We prove that the set $\mathrm{Aut}_{\bar 0}(\mathcal M)$ of automorphisms of $\mathcal M$ can be endowed with the structure of a complex Lie group acting holomorphically on $\mathcal M$,…

We reprove the results of Jordan [18] and Siebert [31] and show that the Lie algebra of polynomial vector fields on an irreducible affine variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not…

In this article, we consider an infinite type domain $\Omega_P$ in $\mathbb C^2$. The purpose of this paper is to investigate the holomorphic vector fields tangent to an infinite type model in $\mathbb C^2$ vanishing at an infinite type…

We prove denominator identities for the periplectic Lie superalgebra $\mathfrak{p}(n)$, thereby completing the problem of finding denominator identities for all simple classical finite-dimensional Lie superalgebras.

If $L$ is a semisimple Lie algebra of vector fields on R^N with a split Cartan subalgebra C, then it is proved that the dimension of the generic orbit of C coincides with the dimension of C. As a consequence one obtains a local canonical…

We consider homotopy actions of a Lie algebroid on a graded manifold, defined as suitable $L_{\infty}$-algebra morphisms. On the "semi-direct product" we construct a homological vector field that projects to the Lie algebroid. Our main…

We study Chevalley-Eilenberg cohomology of physically relevant Lie superalgebras related to supersymmetric theories, providing explicit expressions for their cocycles in terms of their Maurer-Cartan forms. We then include integral forms in…

We provide normal forms for singularities of analytic hypersurfaces in $({\mathbb C}^n,0)$, using holomorphic vector fields.

We establish that for the type I Lie superalgebras $sl(m/n)$ and $osp(2/2n)$, each Kac module admits a 1 parameter family of indecomposable double extensions. The result follows from the explicit evaluation of the $H^1$ Lie superalgebra…

In this paper we show that a (non necessarily integrable) holomorphic plane field on a compact complex manfold $M$ having an infinite number of invariant hypersurfaces must admit a meromorphic first integral $F:M\longrightarrow…

In this paper we give a characterization of real hypersurfaces in noncompact complex two-plane Grassmannian $SU_{2,m}/S(U_2 U_m)$, $m \geq 2$ with Reeb vector field $\xi$ belonging to the maximal quaternionic subbundle $\mathcal Q$. Then it…

We prove that the space of coinvariants of functions on an affine variety by a Lie algebra of vector fields whose flow generates finitely many leaves is finite-dimensional. Cases of the theorem include Poisson (or more generally Jacobi)…

We define the unique (up to normalization) symbol map from the space of linear differential operators on $R^n$ to the space of polynomial on fibers functions on $T^* R^n$, equivariant with respect to the Lie algebra of projective…