Operator quantization of constrained WZNW theories and coset constructions. Abstract Using two WZNW theories for Lie algebras g and h, h ⊂ g, we construct the associative quotient algebra which includes a class of g/h coset primary fields and currents. 1. In a recent article [1] for generic g/h coset conformal field theory [2] a class of Virasoro primary fields and currents was constructed.They...

Let Fn be a free group of rank n and F n the quotient group of Fn by the subgroup [Γn(3),Γn(3)][[Γn(2),Γn(2)],Γn(2)] where Γn(k) denotes the k-th subgroup of the lower central series of the free group Fn. In this paper, we determine the group structure of the graded quotients of the lower central series of the group F n by using a generalized Chen’s integration in free groups. Then we apply it ...

Let X = GM be a finite group factorisation. It is shown that the quantum double D(H) of the associated bicrossproduct Hopf algebra H = kM⊲◭k(G) is itself a bicrossproduct kX⊲◭k(Y ) associated to a group Y X, where Y = G×Mop. This provides a class of bicrossproduct Hopf algebras which are quasitriangular. We also construct a subgroup Y X associated to every order-reversing automorphism θ of X. T...

Let G ⊂ GL(V ) be a complex reductive group where dimV < ∞, and let π : V → V//G be the categorical quotient. Let N := ππ(0) be the null cone of V , and let H be the subgroup of GL(V ) which preserves the ideal I of N . We determine the identity component of H . For adjoint representations we determine H completely. We also investigate the subgroup GF of GL(V ) preserving a fiber F 6= N of π.

A subgroup $H\leq G$ is said to be almost normal if every conjugate of $H$ commensurable $H$. If normal, there a well-defined quotient space $G/H$. We show that group $G$ has type $F_{n+1}$ and contains an coarse $PD_n$ with $e(G/H)=\infty$, then whenever $G'$ quasi-isometric $G$, it $H'$ Moreover, the spaces $G/H$ $G'/H'$ are quasi-isometric. This generalises theorem Mosher-Sageev-Whyte, who p...

In [Ar68], M. Armstrong proved a beautiful result describing fundamental groups of quotient spaces. this paper we prove an analogue Armstrong's theorem in the setting $F$-divided [dS07] and essentially finite [No76] group schemes.