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Let G be a semisimple, simply connected, algebraic group defined over R. The set of real points G of G is not necessarily topologically simply connected, in which case G admits a non–trivial covering ...
Sieve methods in group theory I: Powers in Linear groups
Sieve Property-T Powers Linear groups Finite groups of Lie type
2011/9/14
Abstract: A general sieve method for groups is formulated. It enables one to "measure" subsets of a finitely generated group. As an application we show that if $\Gamma$ is a finitely generated non vir...
Linear estimates for solutions of quadratic equations in free groups
Linear estimates solutions of quadratic equations Group Theory
2011/9/6
Abstract: We prove that in a free group the length of the value of each variable in a minimal solution of a standard quadratic equation is bounded by $2s$ for orientable equation and by $12s^4$ for no...
Homotopy invariance for homology of linear groups: reductions and the rank two case
linear groups the rank two case
2010/11/24
We discuss the problem of homotopy invariance for homology of linear groups. Some reductions we are able to make show that homotopy invariance for linear groups follows from contractibility of a cert...
Subgroups of free idempotent generated semigroups: full linear monoid
Subgroups free idempotent generated semigroups: full linear monoid
2010/12/14
We develop some new topological tools to study maximal subgroups of free idempotent generated semigroups. As an application,we show that the rank 1 component of the free idempotent generated semigroup...
Exponential decay of semigroups for second order non-selfadjoint linear differential equations
Accretive operator sectorial operator C0-semigroup
2011/1/20
The Cauchy problem for second order linear differential equation u′′(t) + Du′(t) + Au(t) = 0
in Hilbert space H with a sectorial operator A and an accretive operator D is studied. Sufficient conditio...
A problem of Kollar and Larsen on finite linear groups and crepant resolutions
Age deviation finite linear groups complex reflection groups
2010/12/6
The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calab...
Hartley´s Theorem on Representations of the General Linear Groups and Classical Groups
subgroups of classical groups representation theory of algebraic groups
2010/2/26
We suggest a new proof of Hartley's theorem on representations of the general linear groups GLn(K) where K is a field. Let H be a subgroup of GLn(K) and E the natural GLn(K)-module. Suppose that the r...