相关论文: Rigidity of graph products of groups

Let B be the generalized braid group associated to some finite complex reflection group. We define a representation of B of dimension the number of reflections of the corresponding reflection group, which generalizes the Krammer…

We prove the first rigidity and classification theorems for crossed product von Neumann algebras given by actions of non-discrete, locally compact groups. We prove that for arbitrary free probability measure preserving actions of connected…

An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that…

We call a group $G$ {\it algorithmically finite} if no algorithm can produce an infinite set of pairwise distinct elements of $G$. We construct examples of recursively presented infinite algorithmically finite groups and study their…

For a finite group $G$, the representation dimension is the smallest integer realizable as the degree of a complex faithful representation of $G$. In this article, we compute representation dimension for some $p$-groups, their direct…

We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…

We introduce special classes of irreducible representations of groups: thick representations and dense representations. Denseness implies thickness, and thickness implies irreducibility. We show that absolute thickness and absolute…

Twin-width is a recently introduced graph parameter with applications in algorithmics, combinatorics, and finite model theory. For graphs of bounded degree, finiteness of twin-width is preserved by quasi-isometry. Thus, through Cayley…

Let K be a p-adic field and let F and G be two formal groups over O_K. We prove that if F and G have infinitely many torsion points in common, then F=G. This follows from a rigidity result: any bounded power series that sends infinitely…

In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.

A graph is one-ended if it contains a ray (a one way infinite path) and whenever we remove a finite number of vertices from the graph then what remains has only one component which contains rays. A vertex $v$ {\em dominates} a ray in the…

A finitely generated solvable group with unbounded iterated identity is constructed.

In this paper we introduced an arithmetic graph function which associates with every group G the directed graph whose vertices corresponds to the divisors of |G|. With the help of such functions we introduced arithmetic graphs of classes of…

A graph is an instrument which is extensively utilized to model various problems in different fields. Up to date, many graphs have been developed to represent algebraic structures, particularly rings in order to study their properties. In…

We prove a discretized sum-product theorem for representations of Lie groups whose Jordan-H\"older decomposition does not contain the trivial representation. This expansion result is used to derive a product theorem in perfect Lie groups.

We consider the problem of realizing a group as the fundamental group of a graph of groups where the vertex groups are restricted to certain classes (for example, coming from a certain finite list of groups, or having bounded geometric…

We state a conjecture on the reduction modulo the defining characteristic of a unipotent representation of a finite reductive group.

If $G$ is a solvable group, we take $\Delta (G)$ to be the character degree graph for $G$ with primes as vertices. We prove that if $\Delta (G)$ is a square, then $G$ must be a direct product.

We survey several notions of Mackey functors and biset functors found in the literature and prove some old and new theorems comparing them. While little here will surprise the experts, we draw a conceptual and unified picture by making…