If Tψ is an ergodic group extension of a weakly mixing transformation T having minimal self-joinings, then it is shown that isomorphism between Tψ and its inverse implies isomorphism between T and T−1. However, if T satisfies the weaker condition of being simple it is shown that that isomorphism between Tψ and its inverse does not imply the isomorphism between T and T−1. This answers a question...

We introduce the linear centralizer method for a passive adversary to extract the shared key in group-theory based key exchange protocols (KEPs). We apply this method to obtain a polynomial time cryptanalysis of the Commutator KEP, introduced by Anshel–Anshel–Goldfeld in 1999 and considered extensively ever since. We also apply this method to the Centralizer KEP, introduced by Shpilrain–Ushakov...

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...

This is the first of two papers determining saturated 2-fusion systems in which centralizer some fully centralized involution contains a component that system large group Lie type over field odd order.

We consider Donovan's conjecture in the context of blocks groups G with defect group D and normal subgroups N◁G such that G=CD(D∩N)N, extending similar results for abelian groups. As an application we show holds form Q8×C2n or Q8×Q8 defined over a discrete valuation ring.

Brauer's centralizer algebras are finite dimensional algebras with a distinguished basis. Each Brauer centralizer algebra contains the group algebra of a symmetric group as a subalgebra and the distinguished basis of the Brauer algebra contains the permutations as a subset. In view of this containment it is desirable to generalize as many known facts concerning the group algebra of the symmetri...

Let F be an algebraically closed field and let G be a semisimple F-algebraic group for which the characteristic of F is very good. If X ∈ Lie(G) = Lie(G)(F) is a nilpotent element in the Lie algebra of G, and if C is the centralizer in G of X, we show that (i) the root datum of a Levi factor of C, and (ii) the component group C/Co both depend only on the Bala-Carter label of X; i.e. both are in...

Femoral stem centralizers were originally designed for double tapered, straight stems. In a slightly modified configuration, the PMMA centralizer is plugged in a hole in the tip of the ABG II femoral prosthesis. The purpose of this study was to determine the effect of the centralizer on the position of the anatomical ABG II stem. Thirty-nine cemented ABG II stems with a centralizer were compare...

Let (G;) be a permutation group of degree n. Let V (G;) be the set of all square matrices of order n which commute with all permutation matrices corresponding to permutations from (G;): V (G;) is a matrix algebra which is called the centralizer algebra of (G;): In this paper we introduce the combinatorial analogue of centralizer algebras, namely coherent (cellular) algebras and consider the pro...

Let G be a compact connected Lie group andH the centralizer of a oneparameter subgroup. We obtain a unified formula that expresses Steenrod operations on Schubert classes in the flag manifold G/H in term of Cartan