We give an exact spectral equivalence between the quantum group invariant XXZ chain with arbitrary left boundary term and the same XXZ chain with purely diagonal boundary terms. This equivalence, and a further one with a link pattern Hamiltonian, can be understood as arising from different representations of the one-boundary Temperley–Lieb algebra. For a system of size L these representations a...

Let X be a non-degenerate left Banach module over a normed algebra A having a bounded approximate left identity. We show that, if A is a left ideal of a larger algebra, then this representation can be extended to a representation of the larger algebra. Based on this result, we study in detail the existence and properties of representations of the various centralizer algebras of A which are comp...

We give a construction of nonsmooth self-dual projective algebraic varieties. They appear as certain projectivized orbit closures for some linear actions of reductive algebraic groups. Applying this construction to adjoint representations, we obtain geometric characterization of distinguished nilpotent elements of semisimple Lie algebras [BC1], [BC2] (i.e., nilpotent elements whose centralizer ...

Throughout this paper, G denotes a simple and simply connected algebraic group over C of rank r and H is a Cartan subgroup, with Lie algebras g = LieG and h = LieH. Let R be the root system of the pair (G,H), W the Weyl group, and Λ ⊆ h the coroot lattice. Fix once and for all a positive Weyl chamber, i.e. a set of simple roots ∆. The geometric invariant theory quotient of g by the adjoint acti...

INTRODUCTION Femoral centralizers in total hip arthroplasty (THA) are designed to improve the neutral implant position and ensure a homogeneous cement mantle without implant-bone impingement. To date there are no data about the cement mantle configuration and implant position after malinsertion, as seen in mini-open approaches or adipose patients with a limited view. The present biomechanical s...

Glauberman’s classical Z∗-theorem is a theorem about involutions of finite groups (i.e. elements of order 2). It is one of the important ingredients for the classification of finite simple groups, which in turn allows to prove the corresponding theorem for elements of arbitrary prime order p. Let us recall the statement: if G is a finite group with a Sylow p-subgroup P , and if x is an element ...

abstract. let r be a 2-torsion free ring with identity. in this paper, first we prove that any jordan left derivation (hence, any left derivation) on the full matrix ringmn(r) (n  2) is identically zero, and any generalized left derivation on this ring is a right centralizer. next, we show that if r is also a prime ring and n  1, then any jordan left derivation on the ring tn(r) of all n×n up...

ly one can define a Lie group as a smooth manifold which is also a group such that inversion and multiplication are smooth maps. A special case we focus on is any (topologically) closed subgroup of any SL(`,R). The major examples of “classical” Lie groups are SL(n,R), SO(m,n) (with g Im,ng = Im,n), SU(m,n) (same as SO but with conjugate transpose and complex elements), and Sp(2m,R) (similar to ...