Related papers: Equations in Burnside groups
Lead by examples we introduce the notions of Hopf algebra and quantum group. We study their geometry and in particular their Lie algebra (of left invariant vectorfields). The examples of the quantum sl(2) Lie algebra and of the quantum…
We construct first examples of discrete geometrically finite subgroups of PU(2,1) which contain parabolic elements, and are isomorphic to surface groups.
Given a periodic quotient of a torsion-free hyperbolic group, we provide a fine lower estimate of the growth function of any sub-semi-group. This generalizes results of Razborov and Safin for free groups.
This manuscript represents the author's PhD dissertation thesis.The first part studies decision problems in Thompson's groups F,T,V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson's…
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…
A connected component of an affine algebraic group is called periodic if all its elements have finite order. We give a characterization of periodic components in terms of automorphisms with finite number of fixed points. It is also…
We provide isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. More generally , we also consider the isomorphism problem for…
This article considers cuspidal curves whose coordinate rings are numerical semigroup algebras. Using a general result about descent of Hopf algebroid structures, their rings of differential operators are shown to be cocommutative and…
In this paper, we study some properties of the outer automorphism group of free Burnside groups of large odd exponent. In particular, we prove that it contains free and free abelian subgroups.
It is known algebraically that any abelian group is a direct sum of a divisible group and a reduced group (See Theorem 21.3 of \cite{Fuchs:abelian-group}). In this paper, conditions to split off rational parts in homotopy types from a given…
We use Bott periodicity to relate previously defined quantum classes to certain "exotic Chern classes" on $BU$. This provides an interesting computational and theoretical framework for some Gromov-Witten invariants connected with…
We show that free-by-free groups satisfying a homological criterion, which we call excessive homology, are incoherent. This class is large in nature, including many examples of hyperbolic and non-hyperbolic free-by-free groups. We apply…
We generalize some results of Paulin and Rips-Sela on endomorphisms of hyperbolic groups to relatively hyperbolic groups, and in particular prove the following. (1) If G is a finitely generated non-elementary relatively hyperbolic group…
We consider skew-commutative subalgebras in Drinfeld-Jimbo quantum groups at a root of unity $\zeta$ generated by primitive power elements. We classify the centrality and commutativity of these skew-polynomial algebras depending on the Lie…
We introduce and study functorial and combinatorial constructions concerning equivariant Burnside groups.
In this Letter, we introduce the Hopf algebra structure of the quantum quaternionic group GL(1,H$_q)$ and discuss the isomorphism between the quantum symplectic group SP$_q(1)$ and the quantum unitary group SU$_q(2)$.
In this paper we study the commensurability of hyperbolic Coxeter groups of finite covolume, providing three necessary conditions for commensurability. Moreover we tackle different topics around the field of definition of a hyperbolic…
We give a necessary and sufficient condition for two Hopf algebras presented as central extensions to be isomorphic, in a suitable setting. We then study the question of isomorphism between the Hopf algebras constructed in 0707.0070v1 as…
A basic point about hyperbolic groups is that they have "spaces at infinity" which are spaces of homogeneous type in the sense of Coifman and Weiss, and with a lot of self-similarity coming from the group. This short survey deals with some…
We start to develop the quantization formalism in a hyperbolic Hilbert space. Generalizing Born's probability interpretation, we found that unitary transformations in such a Hilbert space represent a new class of transformations of…