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Free group algebras in Malcev-Neumann skew fields of fractions
Division rings Malcev-Neumann series Rings and Algebras
2011/9/5
Abstract: Let K be a skew field and (G,<) an ordered group. We show that the skew field generated by the group ring K[G] inside the Malcev-Neumann series ring K((G;<)) contains noncommutative free gro...
On pro-$p$ analogues of limit groups via extensions of centralizers
Group Theory extensions of centralizers limit groups pro-$p$ analogues
2011/9/5
Abstract: We begin a study of a pro-$p$ analogue of limit groups via extensions of centralizers and call $\mathcal{L}$ this new class of pro-$p$ groups. We show that the pro-$p$ groups of $\mathcal{L}...
Rigid abelian groups and the probabilistic method
random construction abelian groups with prescribed endomorphisms probabilistic method Group Theory
2011/9/5
Abstract: The construction of torsion-free abelian groups with prescribed endomorphism rings starting with Corner's seminal work is a well-studied subject in the theory of abelian groups. Usually thes...
On the Cohomology of Deligne-Lusztig Varieties
Cohomology of Deligne-Lusztig Varieties Representation Theory Group Theory
2011/8/31
Abstract: In this paper, we present a conjecture on the degree of unipotent characters in the cohomology of particular Deligne-Lusztig varieties for groups of Lie type, and derive consequences of it. ...
Abstract: For every $\alpha \leq \beta$ in a left neighborhood $[\alpha_0,1]$ of 1, a group $G(\alpha,\beta)$ is constructed, the growth function of which satisfies $\limsup \frac{\log \log b_{G(\alph...
A polynomial bound on solutions of quadratic equations in free groups
polynomial bound quadratic equations free groups Group Theory
2011/8/31
Abstract: We provide polynomial upper bounds on the size of a shortest solution for quadratic equations in a free group. A similar bound is given for parametric solutions in the description of solutio...
A class of II_1 factors with many non conjugate Cartan subalgebras
non conjugate Cartan subalgebras Operator Algebras Dynamical Systems Group Theory
2011/8/26
Abstract: We construct a class of II_1 factors that admit a non smooth family of Cartan subalgebras that are non conjugate by an automorphism. We also construct a II_1 factor that admits uncountably m...
Generalized presentations of infinite groups, in particular of $Aut(F_ω)$
Generalized presentations of infinite groups Group Theory
2011/8/26
Abstract: We develop a theory of generalized presentations of groups. We give generalized presentations of the symmetric group $\Sigma(X)$ for an arbitrary set $X$ and of the automorphism group of the...
Product decompositions in finite simple groups
Product decompositions finite simple groups Group Theory
2011/8/30
Abstract: We propose a general conjecture on decompositions of finite simple groups as products of conjugates of an arbitrary subset. We prove this conjecture for bounded subsets of arbitrary finite s...
The computational complexity of recognising embeddings in finitely presented groups
Finitely presented groups embeddings Kleene’s arithmetical hierarchy decidability universal finitely presented group
2011/8/29
Abstract: We extend a result by Lempp that recognising torsion-freeness for finitely presented groups is $\Pi^{0}_{2}$-complete; we show that the problem of recognising embeddings of finitely presente...
Effective dimension of finite semigroups
dimension of finite semigroups Group Theory Representation Theory
2011/8/29
Abstract: In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general...
Property (T) with respect to non-commutative Lp-spaces
Haagerup non-commutative Lp(M)-spaces property (T) group representations Mazur map
2011/8/29
Abstract: We show that a group with Kazhdan's property $(T)$ has property $(T_{B})$ for $B$ the Haagerup non-commutative $L_{p}(\mathcal{M})$-space associated with a von Neumann algebra $\mathcal{M}$,...
Abstract: Groups acting freely on Z^n-trees (Z^n-free groups) play a key role in the study of non-archimedean group actions. Following Stallings' ideas, we develop graph-theoretic techniques to invest...
Centralizers in R. Thompson's group V_n
Centralizers R. Thompson's group Group Theory Dynamical Systems
2011/8/25
Abstract: Let n be bigger than 1 and let A be an element in the Higman-Thompson group V_n. We study the structure of the centralizer of a in V_n through a careful analysis of the action of the group g...