相关论文: Limits of Baumslag-Solitar groups

A logarithm representation of operators is introduced as well as a concept of pre-infinitesimal generator. Generators of invertible evolution families are represented by the logarithm representation, and a set of operators represented by…

The automorphism group of a regular locally finite tree is shown to admit irreducible Banach representations that are not admissible. The dense subspace of smooth vectors contains no algebraically irreducible component.

To a large class of graphs of groups we associate a C*-algebra universal for generators and relations. We show that this C*-algebra is stably isomorphic to the crossed product induced from the action of the fundamental group of the graph of…

We compute the continuous bounded cohomology of the full automorphism groups of regular trees in all positive degrees, with coefficients arising from any irreducible continuous unitary representations. To the author's knowledge, this seems…

The present paper is a continuation of \cite{jrz} and is devoted to the study of limit varieties of additively idempotent semirings. A limit variety is a nonfinitely based variety whose proper subvarieties are all finitely based. We present…

We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The proof is based on reducing the problem to showing amenability…

In this article, we study the fixed-point subgroups of the solvable Baumslag-Solitar groups $\BS(1,n)= \langle a, t \mid t a t^{-1} = a^{n} \rangle$, $n>1$ of automorphisms and endomorphisms. We also investigate the stabilizers of subgroups…

Building on reduction theorems and dimension bounds for symmetric groups obtained in our earlier work, we classify the irreducible restrictions of representations of the symmetric and alternating groups to proper subgroups. Such…

We give new bounds and asymptotic estimates on the largest Kronecker and induced multiplicities of finite groups. The results apply to large simple groups of Lie type and other groups with few conjugacy classes.

We establish a sharp sufficient condition for groups acting on trees to be highly transitive when the action on the tree is minimal of general type. This gives new examples of highly transitive groups, including icc non-solvable…

Higher-rank graphs are, as the name suggests, higher-dimensional analogues of directed graphs which we will define using category theory. The whole idea of my project was to construct what we call a Baumslag-Solitar graph, a higher-rank…

In this paper we describe the C*-algebras associated to the Baumslag-Solitar groups with the ordering defined by the usual presentations. These are Morita equivalent to the crossed product C*-algebras obtained by letting the group act on…

We prove an accessibility theorem for finite-index splittings of groups. Given a finitely presented group G there is a number n(G) such that, for every reduced locally finite G-tree T with finitely generated stabilizers, T/G has at most…

We consider the infinite symmetric group and its infinite index subgroup given as the stabilizer subgroup of one element under the natural action on a countable set. This inclusion of discrete groups induces a hyperfinite subfactor for each…

In this paper, we prove the K- and L-theoretical Isomorphism Conjecture for Baumslag-Solitar groups with coefficients in an additive category.

We classify irreducible representations of the special linear groups in positive characteristic with small weight multiplicities with respect to the group rank and give estimates for the maximal weight multiplicities. For the natural…

We study the action of groups generated by bounded activity automata with infinite alphabets on their orbital Schreier graphs. We introduce an amenability criterion for such groups based on the recurrence of the first level action. This…

We prove sharp limit theorems on random walks on graphs with values in finite groups. We then apply these results (together with some elementary algebraic geometry, number theory, and representation theory) to finite quotients of lattices…

We consider various classes of Motzkin trees as well as lambda-terms for which we derive asymptotic enumeration results. These classes are defined through various restrictions concerning the unary nodes or abstractions, respectively: We…

We characterize which groups splitting as finite graphs of free groups with cyclic edge groups are residually finite. Such a group $G$ is residually finite if and only if all its Baumslag-Solitar subgroups are residually finite. From a…