We prove that the notion of rigidity (or relative property (T)) for inclusions of finite von Neumann algebras defined in [Po1] is equivalent to a weaker property, in which no “continuity constants” are required. The notion of relative property (T) (or rigidity) for inclusions of finite von Neumann algebras with countable decomposable center was introduced in ([P1]) by requiring that one of the ...

We show how to extend a classic Morita Equivalence Result of Green’s to the C∗-algebras of Fell bundles over transitive groupoids. Specifically, we show that if p : B → G is a saturated Fell bundle over a transitive groupoid G with stability group H = G(u) at u ∈ G(0), then C∗(G,B) is Morita equivalent to C∗(H,C ), where C = B|H . As an application, we show that if p : B → G is a Fell bundle ov...

A C∗-symbolic dynamical system (A, ρ,Σ) is a finite family {ρα}α∈Σ of endomorphisms of a C∗-algebra A with some conditions. It yields a C∗-algebra Oρ from an associated Hilbert C∗-bimodule. In this paper, we will extend the notion of C∗-symbolic dynamical system to C∗-textile dynamical system (A, ρ, η,Σ,Σ, κ) which consists of two C∗-symbolic dynamical systems (A, ρ,Σ) and (A, η,Σ) with certain...

We give an algorithmic way to construct a free bimodule resolution of an algebra admitting a Gröbner base. It enables us to compute the Hochschild (co)homology of the algebra. Let A be a finitely generated algebra over a commutative ring K with a (possibly infinite) Gröbner base G on a free algebra F , that is, A is the quotient F/I(G) with the ideal I(G) of F generated by G. Given a Gröbner ba...

We construct the crossed product A ⋊ ρ̂ of a C*-algebra A with centre Z by an endomorphism ρ , which is special in a weaker sense w.r.t. the notion introduced by Doplicher and Roberts; the notation ρ̂ denotes the tensor C*-category of powers of ρ . We assign to ρ a geometrical invariant, representing a cohomological obstruction for it to be special in the usual sense; such invariant determines ra...

Hypothesis (A): G is a doubly transitive permutation group on a set Q. For 01 E Q, G, has a set Z = {B, , B, ,..., B,}, t > 2, which is a complete set of imprimitivity blocks on Q {a}. Let j Bi / = b > 1 for all i. Denote by H the kernel of G, on .Z and by Ki and K< the subgroups of G, fixing Bi setwise and pointwise respectively, 1 .< i < t. Let /3 E Bl . Here j Q j = 1 + ht. M. D. Atkinson ha...

If G is a finite p-solvable group for some prime p, A a solvable subgroup of the automorphism group of G of order prime to |G| such that A stabilises a p-block b of G and acts trivially on a defect group P of b, then there is a Morita equivalence between the block b and its Watanabe correspondent w(b) of CG(A), given by a bimodule M with vertex ∆P and an endo-permutation module as source, which...

We give experimental support for a conjecture of Louder and Wilton saying that words imprimitivity rank greater than two yield hyperbolic one-relator groups.

This paper gives a p-adic analogue of the Mackey theory, which relates representations of a group of type G = H×tA to systems of imprimitivity.