Related papers: Applications of Lie ring methods to group theory

Let G be a reductive algebraic group over a field of prime characteristic. One can associate to G (or subgroups thereof) its Lie algebra, its Frobenius kernels, and the finite Chevalley group of points over a finite field. The…

We compare and contrast two approaches to the structure theory for Lie pseudo-groups, the first due to Cartan, and the second due to the first two authors. We argue that the latter approach offers certain advantages from both a theoretical…

The usefulness in control theory of the geometric theory of motion on Lie groups and homogeneous spaces will be shown. We quickly review some recent results concerning two methods to deal with these systems, namely, a generalization of the…

The main purpose of these lecture notes is to provide a concise introduction to Lie groups, Lie algebras, and isometric and adjoint actions, aiming mostly at advanced undergraduate and graduate students. In addition, the connection between…

Let $G$ be a compact, connected, and simply-connected Lie group, equipped with a Lie group involution $\sigma_G$ and viewed as a $G$-space with the conjugation action. In this paper, we present a description of the ring structure of the…

I determine the twisted K-theory of all compact simply connected simple Lie groups. The computation reduces via the Freed-Hopkins-Teleman theorem to the CFT prescription, and thus explains why it gives the correct result. Finally I analyze…

This expository article introduces the topic of roots in a compact Lie group. Compared to the many other treatments of this standard topic, I intended for mine to be relatively elementary, example-driven, and free of unnecessary…

Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…

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…

Regular algebraic $K$-theory for groups is a homology theory for discrete groups closely connected (but different from) group homology. It also gives a version of algebraic $K$-theory for rings by the simple functorial mapping assigning to…

The expansion method of Lie algebras by a semigroup or S-expansion is generalized to act directly on the group manifold, and not only at the level of its Lie algebra. The consistency of this generalization with the dual formulation of the…

We consider the Lie algebra associated with the descending central series filtration of the pure braid group of a closed surface of arbitrary genus. R. Bezrukavnikov gave a presentation of this Lie algebra over the rational numbers. We show…

The purpose of this article is to present a survey of our recent results on length commensurable and isospectral locally symmetric spaces. The geometric questions led us to the notion of "weak commensurability" of two Zariski-dense…

This work uses mostly model-theoretic methods to establish new proof-theoretic theorems about several axiomatic theories of truth over KP (Kripke-Platek set theory) and stronger theories, especially ZF (Zermelo-Fraenkel set theory).

Doctoral Thesis, year 2002, about Lie systems and applications in Physics and Control Theory. The text is in English. Advisor: Jos\'e F. Cari\~nena

Using an algebraic point of view we present an introduction to the groupoid theory, that is, we give fundamental properties of groupoids as, uniqueness of inverses and properties of the identities, and study subgroupoids, wide subgroupoids…

Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.

This paper explains the recent developments on the symplectic theory of Hamiltonian completely integrable systems on symplectic 4-manifolds, compact or not. One fundamental ingredient of these developments has been the understanding of…

This is a survey of results on partially commutative groups and partially commutative algebras.

We formulate and prove a twofold generalisation of Lie's second theorem that integrates homomorphisms between formal group laws to homomorphisms between Lie groups. Firstly we generalise classical Lie theory by replacing groups with…