相关论文: Classification of non-degenerate projective variet…

The paper gives the complete characterization of all graded nilpotent Lie algebras with infinite-dimensional Tanaka prolongation as extensions of graded nilpotent Lie algebras of lower dimension by means of a commutative ideal. We introduce…

We call a finite-dimensional complex Lie algebra $\mathfrak{g}$ strongly rigid if its universal enveloping algebra $\Ug$ is rigid as an associative algebra, i.e. every formal associative deformation is equivalent to the trivial deformation.…

In this note, we prove that for any finite dimensional vector space $V$ over an algebraically closed field $k$, and for any finite subgroup $G$ of $GL(V)$ which is either solvable or is generated by pseudo reflections such that the $|G|$ is…

Let $G$ be a simple real Lie group with maximal parabolic subgroup $P$ whose nilradical is abelian. Then $X=G/P$ is called a symmetric $R$-space. We study the degenerate principal series representations of $G$ on $C^\infty(X)$ in the case…

Let $(G,\tau)$ be a finite-dimensional Lie group with an involutive automorphism $\tau$ of $G$ and let $\mathfrak g = \mathfrak h \oplus \mathfrak q $ be its corresponding Lie algebra decomposition. We show that every non-degenerate…

We first give a deformation theory of integrable distributions of codimension 1. We define a parametrization of families of smooth hypersurfaces near a Levi flat hypersurface L such that the Levi flat deformations are given by the solutions…

Let G = Aut(T) be the automorphism group of a regular tree T. We study continuous irreducible representations of G that preserve a continuous strongly nondegenerate sesquilinear form of finite index on a Hilbert space. These are already…

We classify real and complex infinite-dimensional narrow positively graded Lie algebras ${\mathfrak g}=\oplus_{i=1}^{{+}\infty}{\mathfrak g}_i$ with properties $$ [{\mathfrak g}_1, {\mathfrak g}_i]={\mathfrak g}_{i{+}1}, \; \dim{{\mathfrak…

Let k be a field, let G be an affine algebraic k-group and V a finite-dimensional G-module. We say V is rigid if the socle series and radical series coincide for the action of G on each indecomposable summand of V; say V is geometrically…

When $G$ is a complex reductive algebraic group and $G/K$ is a reductive symmetric space, the decomposition of $\C[G/K]$ as a $K$-module was obtained (in a non-constructive way) by Richardson, generalizing the celebrated result of…

Given a finite dimensional Lie algebra $\mathfrak{g}$, let $\Gamma_\circ(\mathfrak{g})$ be the set of irreducible $\mathfrak{g}$-modules with non-vanishing cohomology. We prove that a $\mathfrak{g}$-module $V$ belongs to…

Given a (singular, codimension 1) holomorphic foliation F on a complex projective manifold X, we study the group PsAut(X, F) of pseudo-automorphisms of X which preserve F ; more precisely, we seek sufficient conditions for a finite index…

We show the correspondence between left invariant flat projective structures on Lie groups and certain prehomogeneous vector spaces. Moreover by using the classification theory of prehomogeneous vector spaces, we classify complex Lie groups…

This paper analyses non-regular $|2|$-graded geometries, and show that they share many of the properties of regular geometries -- the existence of a unique normal Cartan connection encoding the structure, the harmonic curvature as…

In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…

We prove a number of results on integrability and extendability of Lie algebras of unbounded skew-symmetric operators with common dense domain in Hilbert space. By integrability for a Lie algebra $\mathfrak{g}$, we mean that there is an…

A Rota-Baxter Lie algebra $\mathfrak{g}_T$ is a Lie algebra $\mathfrak{g}$ equipped with a Rota-Baxter operator $T : \mathfrak{g} \rightarrow \mathfrak{g}$. In this paper, we consider non-abelian extensions of a Rota-Baxter Lie algebra…

Let $V$ be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group $G$ of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for $G$ and the…

We describe a class (called regular) of invariant generalized complex structures on a real semisimple Lie group G. The problem reduces to the description of admissible pairs (\gk, \omega), where \gk is an appropriate regular subalgebra of…

The theory of algebras with polynomial identities has developed significantly, with special attention devoted to the classification of varieties according to the asymptotic behavior of their codimension sequences. This sequence is a…