相关论文: Adjoint orbit types of compact exceptional Lie gro…

Riemannian geodesic orbit spaces (G/H,g) are natural generalizations of symmetric spaces, defined by the property that their geodesics are orbits of one-parameter subgroups of G. We study the geodesic orbit spaces of the form (G/S,g), where…

We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group $\mathrm{String}(n)$. A Lie 2-algebra is a categorified version of a Lie algebra where the Jacobi identity holds up…

We introduce the symplectic group $\mathrm{Sp}_2(G, \sigma)$ associated to a Lie subgroup $G$ of a (possibly noncommutative) associative algebra $A$ equipped with an anti-involution $\sigma$. Our construction recovers several classical Lie…

Our goal is to find a representative of each orbit of the coadjoint action of the generalized Galile group on the dual of its Lie algebra. Our line of argument follows that of Cushman and van der Kallen, but differs in the details.

We construct Lie algebras arising from cubic norm pairs over arbitrary commutative base rings. Such Lie algebras admit a grading by a root system of type $G_2$, and when the cubic norm pair is a cubic Jordan matrix algebra, the…

In this paper we construct a deformation quantization of the algebra of polynomials of an arbitrary (regular and non regular) coadjoint orbit of a compact semisimple Lie group. The deformed algebra is given as a quotient of the enveloping…

The compact simply connected Riemannian 4-symmetric spaces were classified by J.A. Jim{\'{e}}nez according to type of the Lie algebras. As homogeneous manifolds, these spaces are of the form $G/H$, where $G$ is a connected compact simple…

Some features of Cayley algebras (or algebras of octonions) and their Lie algebras of derivations over fields of low characteristic are presented. More specifically, over fields of characteristic $7$, explicit embeddings of any twisted form…

We characterise the groupoid $C^*$-algebras associated to the transformation groupoids of injective actions of discrete countable Ore semi-groups on compact topological spaces in terms of the reduced crossed product from the dual actions,…

Let $\mathcal G_2$ denote the affine group $GL(2,\mathbb Z) \ltimes \mathbb Z^{2}$. For every point $x=(x_1,x_2) \in \R2$ let $\orb(x)=\{y\in\R2\mid y=\gamma(x)$ for some $\gamma \in \mathcal{G}_2 \}$. Let $G_{x}$ be the subgroup of the…

We consider a class of homogeneous manifolds including all semisimple coadjoint orbits. We describe manifolds of that class admitting deformation q uantizations equivariant under the action of $G$ and the corresponding quantum group. We…

The main result asserts: Let $G$ be a reductive, affine algebraic group and let $(\rho ,V)$ be a regular representation of $G$. Let $X$ be an irreducible $\mathbb{C}^{ \times } G$ invariant Zariski closed subset such that $G$ has a closed…

This article contains an investigation of the equitable basis for the Lie algebra sl_2. Denoting this basis by {x,y,z}, we have [x,y] = 2x + 2y, [y,z] = 2y + 2z, [z, x] = 2z + 2x. One focus of our study is the group of automorphisms G…

We classify group gradings on the simple Lie algebra $L$ of type $D_4$ over an algebraically closed field of characteristic different from 2: fine gradings up to equivalence and $G$-gradings, with a fixed group $G$, up to isomorphism. For…

We show that untwisted respectively twisted conjugacy classes of a compact and simply connected Lie group which satisfy a certain integrality condition correspond naturally to irreducible highest weight representations of the corresponding…

Let $M$ be a $G$-covering of a nilpotent orbit in $\g$ where $G$ is a complex semisimple Lie group and $\g=\text{Lie}(G)$. We prove that under Poisson bracket the space $R[2]$ of homogeneous functions on $M$ of degree 2 is the unique…

We study the existence of certain characteristically nilpotent Lie algebras with flat coadjoint orbits. Their connected, simply connected Lie groups admit square-integrable representations modulo the center. There are many examples of…

We develop a semigroup approach to representation theory for pro-Lie groups satisfying suitable amenability conditions. As an application of our approach, we establish a one-to-one correspondence between equivalence classes of unitary…

We consider all connected and simply connected 7-dimensional Lie groups whose Lie algebras have nilradical $\g_{5,2} = \s \{X_1, X_2, X_3, X_4, X_5 \colon [X_1, X_2] = X_4, [X_1, X_3] = X_5\}$ of Dixmier. First, we give a geometric…

The compact simply connected Riemannian 4-symmetric spaces were classified by J.A. Jim{\'{e}}nez according to type of the Lie algebras. As homogeneous manifolds, these spaces are of the form $G/H$, where $G$ is a connected compact simple…