Related papers: Conjugacy classes in discrete Heisenberg groups

Determining the length of short conjugators in a group can be considered as an effective version of the conjugacy problem. The conjugacy length function provides a measure for these lengths. We study the behaviour of conjugacy length…

We investigate the structure of subspaces of a Hilbert space that are invariant under unitary representations of a discrete group. We work with square integrable representations, and we show that they are those for which we can construct an…

Conjugations in space $L^2$ of the unit circle commuting with multiplication by $z$ or intertwining multiplications by $z$ and $\bar z$ are characterized. We also study their behaviour with respect to the Hardy space, subspaces invariant…

We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…

We present the notion of injective hom-complexity, leading to a connection between the covering number of a group and the sectional number of a group homomorphism, and provide estimates for computing this invariant.

The matched pair theory (of groups) is studied for a class of quasigroups; namely, the $m$-inverse property loops. The theory is upgraded to the Hopf level, and the "$m$-invertible Hopf quasigroups" are introduced.

We develop the theory of probabilistic variants of the one-category and diagonal topological complexity, which bound the classical LS-category and topological complexity from below. Unlike any other classical or probabilistic invariants,…

We characterize the group property of being with infinite conjugacy classes (or icc, i.e. \not= 1 and of which all conjugacy classes except 1 are infinite) for finite extensions of group.

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…

We evaluate one-dimensional representations of quantum symmetric conjugacy classes of classical matrix groups along with their quantum stabilizer subgroups.

We consider a particular class of Garside groups, which we call circular groups. We mainly prove that roots are unique up to conjugacy in circular groups. This allows us to completely classify these groups up to isomorphism. As a…

We extend the notion of induced conjugacy classes in reductive groups, introduced by Lusztig and Spaltenstein for unipotent classes, to arbitrary classes. We study properties of equivariant fibrations of prehomogeneous affine spaces,…

In [BGLM] and [GLNP] it was conjectured that if $H$ is a simple Lie group of real rank at least 2, then the number of conjugacy classes of (arithmetic) lattices in $H$ of covolume at most $x$ is $x^{(\gamma(H)+o(1))\log x/\log\log x}$ where…

Condensed mathematics as developed by Clausen and Scholze yields a version of derived functors over the category of continuous $G$-modules for a Hausdorff topological group $G$. We study the resulting notion of group cohomology and its…

In this paper, we study the structure of finite groups with a large number of conjugacy classes of $p$-elements for some prime $p$. As consequences, we obtain some new criteria for the existence of normal $p$-complements in finite groups.

We consider the three-dimensional Heisenberg group, equipped with any left-invariant metric, either Lorentzian or Riemannian. We completely classify their affine vector fields and investigate their relationship with Killing vector fields…

In this article we consider a restricted orbital counting problem for the action of certain discrete groups on suitable spaces. In particular, we present asymptotics for counting those points in an orbit restricted to a single conjugacy…

We investigate two "categorified" braid conjugacy class invariants, one coming from Khovanov homology and the other from Heegaard Floer homology. We prove that each yields a solution to the word problem but not the conjugacy problem in the…

We introduce and study model-theoretic connected components of rings as an analogue of model-theoretic connected components of definable groups. We develop their basic theory and use them to describe both the definable and classical Bohr…

The notion of inner linear Hopf algebra is a generalization of the notion of discrete linear group. In this paper, we prove two general results that enable us to enlarge the class of Hopf algebras that are known to be inner linear: the…