Related papers: L.G. Kov\'acs and linear groups

We incorporate nonlinear covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. This L-group is an extension of the absolute Galois group of a local or global field $F$ by a complex…

We develop aspects of geometric control theory on Lie groups G which may be infinite dimensional, and on smooth G-manifolds M modelled on locally convex spaces. As a tool, we discuss existence and uniqueness questions for differential…

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…

Tannaka's Theorem states that a linear algebraic group G is determined by the category of finite dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category…

The study of localizations of groups has concentrated on group theoretic properties which are preserved by localization. In this paper we look at finitely generated soluble groups and determine when the local groups associated with them are…

We study a few basic properties of Banach-Lie groupoids and algebroids, adapting some classical results on finite dimensional Lie groupoids. As an illustration of the general theory, we show that the notion of locally transitive Banach-Lie…

We analyze log-algebraic power series identities for formal groups of elliptic curves over $\mathbb{Q}$ which arise from modular parametrizations. We further investigate applications to special values of elliptic curve $L$-functions.

In this book, I explored differential equations for operation in Lie group and for representations of group Lie in a vector space.

Linear algebra represents, with calculus, the two main mathematical subjects taught in science universities. However this teaching has always been difficult. In the last two decades, it became an active area for research works in…

In this paper we extend the results on controllability of linear systems obtained in "Controllability of linear systems on solvable Lie groups", from solvable Lie groups to Lie groups with finite semisimple center.

Generalizing a construction of Wolfgang L\"uck and Bob Oliver, we define a good equivariant cohomology theory on the category of proper G-CW complexes when G is an arbitrary Lie group (possibly non-compact). This is done by constructing an…

Computations in the cohomology of finite groups.

Stochastic field equations for linearized gravity are presented. The theory is compared with the usual quantum field theory and questions of Lorentz covariance are discussed. The classical radiation approximation is also presented.

The paper has a form of a talk on the given topic. It consists of three parts. The first part of the paper contains main notions, the second one is devoted to logical geometry, the third part describes types and isotypeness. The problems…

The survey presents the main developments obtained over the last decade regarding pointwise ergodic theorems for measure preserving actions of locally compact groups. The survey includes an exposition of the solutions to a number of long…

Computability theory is used to evaluate the complexity of classifying various kinds of Lebesgue spaces and associated isometric isomorphism problems.

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…

Clifford theory establishes a relation between the representation theory of a finite group and its normal subgroups. In this paper, we establish the Clifford theory for the modular representations of finite groups. The proofs are based on…

Recent results on the linearity of braid groups are extended in two ways. We generalize the Lawrence Krammer representation as well as Krammer's faithfulness proof for this linear representation to Artin groups of finite type.

This is a survey of methods developed in the last few years to prove results on growth in non-commutative groups. These techniques have their roots in both additive combinatorics and group theory, as well as other fields. We discuss linear…