By studying certain kind of centralizer algebras of the affine Schur algebra S̃(n, r) we show that S̃(n, r) is Noetherian and we determine its center. Assuming n ≥ r, we show that S̃(n+ 1, r) is Morita equivalent to S̃(n, r), and the Schur functor is an equivalence under certain conditions.

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.

The mixed braid groups are the subgroups of Artin braid groups whose elements preserve a given partition of the base points. We prove that the centralizer of any braid can be expressed in terms of semidirect and direct products of mixed braid groups. Then we construct a generating set of the centralizer of any braid on n strands, which has at most k(k+1) 2 elements if n = 2k , and at most k(k+3...

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.

Recent results on the Racah algebra $\mathcal{R}_n$ of rank $n - 2$ are reviewed. is defined in terms generators and relations sits centralizer diagonal action $\mathfrak{su}(1,1)$ $\mathcal{U}(\mathfrak{su}(1,1))^{\otimes n}$. Its connections with multivariate polynomials discussed. It shown to be symmetry generic superintegrable model $ (n-1)$ sphere a number interesting realizations provided.

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...