Related papers: Lie groups and Lie algebras
We show that there is an equivalence of $\infty$-categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the $\infty$-category of curved Lie algebras using the homotopy theory of…
An infinite-dimensional Lie Algebra is proposed which includes, in its subalgebras and limits, most Lie Algebras routinely utilized in physics. It relies on the finite oscillator Lie group, and appears applicable to twisted noncommutative…
The adjoint action of a finite group of Lie type on its Lie algebra is studied. A simple formula is conjectured for the number of split semisimple orbits of a given genus. This conjecture is proved for type A, and partial results are…
A Lie algebra $L$ is said to be $(\Theta_{n},sl_{n})$-graded if it contains a simple subalgebra $\mathfrak{g}$ isomorphic to $sl_{n}$ such that the $\mathfrak{g}$-module $L$ decomposes into copies of the adjoint module, the trivial module,…
We explore to what extent the underlying variety of a connected algebraic group or the underlying manifold of a real Lie group determines its group structure.
The aim of this lecture is to give a pedagogical explanation of the notion of a Poisson Lie structure on the external algebra of a Poisson Lie group which was introduced in our previous papers. Using this notion as a guide we construct…
This is an expanded version of my talk given at the workshop "Hot Topics: Thin Groups and Super-strong Approximation" (MSRI, Berkeley, February 6-10, 2012).
The index of a Lie algebra is an important invariant which arises in several areas, e.g. in the study of coadjoint orbits for a Lie group, in invariant theory and in representation theory. We study the index for several classes of nilpotent…
In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and…
We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion…
We call a unital locally convex algebra $A$ a continuous inverse algebra if its unit group $A^\times$ is open and inversion is a continuous map. For any smooth action of a, possibly infinite-dimensional, connected Lie group $G$ on a…
The purpose of this paper is to generalize some results on $n$-Lie algebras and $n$-Hom-Lie algebras to $n$-Hom-Lie color algebras. Then we introduce and give some constructions of $n$-Hom-Lie color algebras.
In this paper we define a new algebraic object: the disguised-groups. We show the main properties of the disguised-groups and, as a consequence, we will see that disguised-groups coincide with regular semigroups. We prove many of the…
This is an overview of the basics of inverse semigroup theory written for the Workshop on Semigroups and Categories held at the University of Ottawa in 2010.
This is a set of lecture notes for a course given at the 2005 Summer School in Poisson Geometry held at ICTP-Trieste.
In this article, we introduce mock-Lie superalgebras, we give some definitions, properties, constructions, and we study their representations. Moreover we introduce pseudo-euclidean mock-Lie superalgebras which are mock-Lie superalgebras…
We study \'etale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, such as the…
The aim of this paper is to introduce and study Lie algebras and Lie groups over noncommutative rings. For any Lie algebra $\gg$ sitting inside an associative algebra $A$ and any associative algebra $\FF$ we introduce and study the algebra…
In this article we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra of sections of the associated Lie…
This paper is a revised version of a previously posted paper in arxiv. The authors posted it as a new submission by mistake. The latest version of the paper can be found at arXiv:math-ph/0512003v2