Related papers: Frobenius groups of automorphisms and their fixed …

We prove that the Heisenberg groups can be distinguished from the other connected and simply connected Lie groups via their group $C^*$-algebras. The main step of the proof is a characterization of the nilpotent Lie groups among the…

Let $G$ be a torsion-free, finitely-generated, nilpotent and metabelian group. In this work we show that $G$ embeds into the group of orientation preserving $C^{1+\alpha}$-diffeomorphisms of the compact interval, for all $\alpha< 1/k$ where…

It is known that a finite group with an automorphism $\varphi$ of coprime order has a soluble radical of $(|\varphi|,|C_G(\varphi)|)$-bounded Fitting height and index. We extend this classic result as follows. Let $f(x) = a_0 + a_1 \cdot x…

We prove that an arbitrary compact metrizable group can be realized as the automorphism group of a graphing; this is a continuous analogue to Frucht's theorem recovering arbitrary finite groups are automorphism groups of finite graphs. The…

Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…

Let $G$ be an infinite simple group of finite Morley rank and $\alpha$ a supertight automorphism of $G$ so that the fixed point subgroup $P_n:=C_G(\alpha^n)$ is pseudofinite for all $n\in \mathbb{N}\setminus\{0\}$. It is know (using CFSG)…

A left Engel sink of an element $g$ of a group $G$ is a set ${\mathscr E}(g)$ such that for every $x\in G$ all sufficiently long commutators $[...[[x,g],g],\dots ,g]$ belong to ${\mathscr E}(g)$. (Thus, $g$ is a left Engel element precisely…

Let $g$ be an element of a group $G$. For a positive integer $n$, let $E_n(g)$ be the subgroup generated by all commutators $[...[[x,g],g],\dots ,g]$ over $x\in G$, where $g$ is repeated $n$ times. We prove that if $G$ is a profinite group…

We characterize a natural class of modular categories of prime power Frobenius-Perron dimension as representation categories of twisted doubles of finite p-groups. We also show that a nilpotent braided fusion category C admits an analogue…

We show that group C*-algebras of finitely generated, nilpotent groups have finite nuclear dimension. It then follows, from a string of deep results, that the C*-algebra $A$ generated by an irreducible representation of such a group has…

For locally compact groups G and H let A(G) denote the Fourier algebra of G and B(H) the Fourier-Stieltjes algebra of H. Any continuous piecewise affine map alpha:Y -> G (where Y is an element of the open coset ring of H) induces a…

Let $\bfG$ be a connected reductive algebraic group defined over $\F_q$, where $q$ is a power of a prime $p$ that is good for $\bfG$. Let $F$ be the Frobenius morphism associated with the $\FF_q$-structure on $\bfG$ and set $G = \bfG^F$,…

Let $A$ be a finite nilpotent group acting fixed point freely on the finite (solvable) group $G$ by automorphisms. It is conjectured that the nilpotent length of $G$ is bounded above by $\ell(A)$, the number of primes dividing the order of…

Let E be a second-countable, locally compact, Hausdorff groupoid equipped with an action of T such that G:=E/T is a principal groupoid with Haar system \lambda. The twisted groupoid C*-algebra C*(E;G,\lambda) is a quotient of the C*-algebra…

The paper presents the complete classification of Automorphic Lie Algebras based on $\mathfrak{sl}_n (\mathbb{C})$, where the symmetry group $G$ is finite and the orbit is any of the exceptional $G$-orbits in $\overline{\mathbb{C}}$. A key…

Given a directed graph $E$ and an associative unital ring $R$ one may define the Leavitt path algebra with coefficients in $R$, denoted by $L_R(E)$. For an arbitrary group $G$, $L_R(E)$ can be viewed as a $G$-graded ring. In this article,…

Clifford theory relates the representation theory of finite groups to those of a fixed normal subgroup by means of induction and restriction, which is an adjoint pair of functors. We generalize this result to the situation of a…

Let $G$ be a reductive algebraic group scheme defined over $\mathbb{F}_p$ and let $G_1$ denote the Frobenius kernel of $G$. To each finite-dimensional $G$-module $M$, one can define the support variety $V_{G_1}(M)$, which can be regarded as…

Let G be a finitely generated relatively hyperbolic group. We show that if no peripheral subgroup of G is hyperbolic relative to a collection of proper subgroups, then the fixed subgroup of every automorphism of G is relatively quasiconvex.…

Given integers $d\ge 3$ and $N\ge 3$. Let $G$ be a finite abelian group acting faithfully and linearly on a smooth hypersurface of degree $d$ in the complex projective space $\mathbb{P}^{N-1}$. Suppose $G\subset PGL(N, \mathbb{C})$ can be…