Related papers: Defining amalgams of compact Lie groups

Let $\mathfrak{g}$ be a finite-dimensional simple Lie algebra over an algebraically closed field of characteristic 0. In this paper we classify all regular decompositions of $\mathfrak{g}$ and its irreducible root system $\Delta$. A regular…

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…

A new class of integrable mappings and chains is introduced. Corresponding $(1+2)$ integrable systems invariant with respect to such discrete transformations are presented in an explicit form. Their soliton-type solutions are constructed in…

The notion of defining relations is well-defined for any nilpotent Lie algebra. Therefore a conventional way to present a simple Lie algebra G is by splitting it into the direct sum of a commutative Cartan subalgebra and two maximal…

An irreducible representation of a reductive Lie algebra, when restricted to a Cartan subalgebra, decomposes into weights with multiplicity. The first part of this paper outlines a procedure to compute symmetric polynomials (e.g., power…

We classify closed abelian subgroups of a compact simple Lie group of adjoint type and of type E having centralizer of the same dimension as the dimension of the subgroup and describe Weyl groups of maximal abelian subgroups.

Let $G$ be a simply connected semisimple algebraic group over $\mathbb{C}$ and let $\rho :G\rightarrow GL(V_\lambda)$ be an irreducible representation of highest weight $\lambda$. Suppose that $\rho$ has finite kernel. Springer defined…

The action of a torus group $T$ on a symplectic toric manifold $(M,\omega)$ often extends to an effective action of a (non-abelian) compact Lie group $G$. We may think of $T$ and $G$ as compact Lie subgroups of the symplectomorphism group…

Given a compact semisimple Lie group $G$ of rank $r$, and a parameter $q>0$, we can define new associativity morphisms in Rep(Gq) using a 3-cocycle $\Phi$ on the dual of the center of G, thus getting a new tensor category Rep(Gq)$^\Phi$.…

We replace the group of group-like elements of the quantized enveloping algebra $U_q({\frak{g}})$ of a finite dimensional semisimple Lie algebra ${\frak g}$ by some regular monoid and get the weak Hopf algebra ${\frak{w}}_q^{\sf d}({\frak…

In this paper, we continue our study of the class of diagram groups. Simply speaking, a diagram is a labelled plane graph bounded by a pair of paths (the top path and the bottom path). To multiply two diagrams, one simply identifies the top…

Let $S$ be a subsemigroup of a second countable locally compact group $G$, such that $S^{-1}S=G$. We consider the $C^*$-algebra $C^*_\delta(S)$ generated by the operators of translation by all elements of $S$ in $L^2(S)$. We show that this…

Let $G$ be a complex reductive connected algebraic group equipped with the Sklyanin bracket. A classification of Poisson homogeneous $G$-spaces with connected isotropy subgroups is given. This result is based on Drinfeld's correspondence…

We classify the almost abelian Lie algebras $\mathfrak g_A=\mathbb R e_0 \ltimes_A \mathbb R^{2n-1}$ admitting complex or symplectic structures. The matrix $A\in M(2n-1,\mathbb R )$ encodes the adjoint action of $e_0$ on the abelian ideal…

We define and study an analogue of the Baum-Connes assembly map for complex semisimple quantum groups, that is, Drinfeld doubles of $ q $-deformations of compact semisimple Lie groups. Our starting point is the deformation picture of the…

Let $\mathfrak{g}$ be a Lie algebra over an algebraically closed field $\Bbbk$ of characteristic zero. Define the universal grading group $\mathcal{C}(\mathfrak{g})$ as having one generator $g_{\rho}$ for each irreducible…

In this article, we construct infinite families $(G_n)_{n \in \mathbb{N}}$ of finite simple groups $G_n$ of Lie type, such that the rank of $G_n$ strictly increases as $n$ tends to infinity, and such that each $G_n$ is a quotient of the…

The dual Lie bialgebra of a certain ``quasitriangular'' Lie bialgebra structure on the Heisenberg Lie algebra determines a (non-compact) Poisson--Lie group G. The compatible Poisson bracket on G is non-linear, but it can still be realized…

In Kac's classification of finite-dimensional Lie superalgebras, the contragredient ones can be constructed from Dynkin diagrams similar to those of the simple finite-dimensional Lie algebras, but with additional types of nodes. For…

Polynomials in this paper are defined starting from a compact semisimple Lie group. A known classification of maximal, semisimple subgroups of simple Lie groups is used to select the cases to be considered here. A general method is…