相关论文: Notes on Lie algebras and Lie groups

It is shown that there is a $C^*$-algebraic quantum group related to any double Lie group. An algebra underlying this quantum group is an algebra of a differential groupoid naturally associated with a double Lie group

We construct the Lie algebra of an n-Lie algebra and we also define the notion of cohomology of an n-Lie algebra.

This expository note outlines why it is sometimes useful to consider the bigraded type A link homology theories as associated with the Lie algebras gl(N) instead of sl(N).

We present an application of Hodge theory towards the study of irreducible unitary representations of reductive Lie groups. We describe a conjecture about such representations and discuss some progress towards its proof.

These are the notes from my courses on the arithmetic of quadratic forms.

Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…

We give a concise introduction to (discrete) algebras arising from \'etale groupoids, (aka Steinberg algebras) and describe their close relationship with groupoid C*-algebras. Their connection to partial group rings via inverse semigroups…

We characterize, up to Lie isomorphism, the real Lie groups that are definable in an o-minimal expansion of the real field.

This note surveys how the exterior algebra and deformations or quotients of it, gives rise to centrally important notions in five domains of mathematics: Combinatorics, Topology, Lie theory, Mathematical physics, and Algebraic geometry.

This paper surveys recent work on Lie algebras of differential operators and their application to the construction of quasi-exactly solvable Schroedinger operators.

In this talk we introduce several topics in combinatorial number theory which are related to groups; the topics include combinatorial aspects of covers of groups by cosets, and also restricted sumsets and zero-sum problems on abelian…

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…

Since 1870s, scientists have been taking deep insight into Lie groups and Lie algebras. With the development of Lie theory, Lie groups have got profound significance in many branches of mathematics and physics. In Lie theory, exponential…

This is a brief introduction to the theories of Lie groups, algebraic groups and their discrete subgroups, which is based on a lecture series given during the Summer School held in the Banach Centre in Poland in Summer 2011.

This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…

This note started out as a letter to J\"urgen Ritter and is brief attempt to entice some number theorists to study hom-Lie algebras.

These are the lecture notes of a 2-hour mini-course on Lie groups over local fields presented at the "Workshop on Totally Disconnected Groups, Graphs and Geometry" at the Heinrich-Fabri-Institut Blaubeuren in May 2007. The goal of the notes…

These notes deal with finite-dimensional normed algegras, some basic examples, and the definition of the spectrum.

In this paper, we attempt to develop the Schreier theory for two special types extensions of multiplicative Lie algebras.

The quasi-filiform Lie algebras of nonzero rank are described. The classifications of filiform and quasi-filiform naturally graded algebras are corrected.