相关论文: Pseudoriemannian Nilpotent Lie Groups

We establish a surprising correspondence between groups definable in o-minimal structures and linear algebraic groups, in the nilpotent case. It turns out that in the o-minimal context, like for finite groups, nilpotency is equivalent to…

We survey a few results on the boundedness of operators arising from the Weyl-Pedersen calculus associated with irreducible representations of nilpotent Lie groups.

These pages covers my expository talks during the seminar "Sub-Riemannian geometry and Lie groups" organised by the author and Tudor Ratiu at the Mathematics Department, EPFL, 2001. However, this is the first part of three, in preparation,…

In this article we provide evidence for a well-known conjecture which states that quasi-isometric simply-connected nilpotent Lie groups are isomorphic. We do so by constructing new examples which are rigid in the sense that whenever they…

This note is a reproduction of the well known and historically significant series of notes called "The Edmonton Notes on Nilpotent Groups" based on lectures given by Philip Hall using the copy found in the Queen Mary College Mathematics…

In this paper, several theorems of Macdonald \cite{Mac1961,Mac1962} on the varieties of nilpotent groups will be generalized to the case of Lie rings. We consider three varieties of Lie rings of any characteristic associated with some…

The paper studies nilpotent $n$-Lie superalgebras. More specifically speaking, we first prove Engel's theorem for $n$-Lie superalgebras. Second, we research some properties of nilpotent $n$-Lie superalgebras, Finally, we give several…

Prepared for the Quantum Field Theory section of the Encyclopedia of Mathematical Physics, Elsevier, 2006. A brief introduction to the methodology and techniques of perturbative relativistic quantum field theory is presented.

This article will appear in the Encyclopedia of Mathematical Physics (Elsevier, 2006) and follows its referencing guidelines.

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 is a submission to the Encyclopedia of Mathematical Physics (Elsevier, 2006) and conforms to its referencing guidelines.

This paper has been withdrawn by the authors; it will be incorporated into part I of the series (in preparation).

We develop the structure theory of symplectic Lie groups based on the study of their isotropic normal subgroups. The article consists of three main parts. In the first part we show that every symplectic Lie group admits a sequence of…

The original version of the paper was published in Contemporary Mathematics 378 ``Groups, Languages, Algorithms''; 2005, pp. 319-348. This is a modified version with Appendix that holds a corrected formulation of Proposition 4.1.

We give the number of nilpotent orbits in the Lie algebras of orthogonal groups under the adjoint action of the groups over $\tF_{2^n}$. Let $G$ be an adjoint algebraic group of type $B,C$ or $D$ defined over an algebraically closed field…

In the paper are proved theorems, which amplify the results of my paper "On the difference equation of Poincare type (Part 3)", Max-Plank-Institut fuer Mathematik, Bonn, Preprint Series, 2004, 09, 1-34.

The structure of a group which is not nilpotent but all of whose proper subgroups are nilpotent has interested the researches of several authors both in the finite case and in the infinite case. The present paper generalizes some classic…

In this article we study the homology of nilpotent groups. In particular a certain vanishing result for the homology and cohomology of nilpotent groups is proved.

A compendium for outsiders.

This is an old article of 2000. Its aim is to illustrate how a Lie-theoretic result of Zelmanov enables one to treat various problems in group theory.