For each field k, natural number n and parameter δ ∈ k, the Brauer algebra Bn(δ) is a finite dimensional algebra, with a basis of pair partitions of the set {1, 2, ..., 2n} [2]. Indeed there is a Z[δ]-algebra BZ n (for δ indeterminate), free of finite rank as a Z[δ]-module, that passes to each Brauer algebra by the natural base change; and a collection of modules {∆Z(λ)}λ∈Λn for this algebra th...

In this paper we study the partial Brauer C-algebras Rn(δ, δ ), where n ∈ N and δ, δ ∈ C. We show that these algebras are generically semisimple, construct the Specht modules and determine the Specht module restriction rules for the restriction Rn−1 →֒ Rn. We also determine the corresponding decomposition matrix, and the Cartan decomposition matrix.

Compatible topologies and bornologies on modules are introduced and studied.

Let X and Y be Hilbert C *-modules over a C *-algebra, and ϕ : X × Y → [0, ∞) be a function. A (not necessarily linear) mapping f : X → Y is called a ϕ-perturbed adjointable mapping if there exists a (not necessarily linear) mapping g : Y → X such that In this paper, we investigate the stability of adjointable mappings on Hilbert C *-modules and discuss the case where the modules are self-dual....

We define a simple, explicit map sending a morphism f : M → N of pointwise finite dimensional persistence modules to a matching between the barcodes of M and N . Our main result is that, in a precise sense, the quality of this matching is tightly controlled by the lengths of the longest intervals in the barcodes of ker f and coker f . As an immediate corollary, we obtain a new proof of the alge...