In this paper, we investigate problems about isomorphisms and automorphism groups of Cayley digraphs. A class of Cayley digraphs, corresponding to the so-called CDI-subsets, for which the isomorphisms are uniquely determined by the group automorphisms is characterized. Their automorphism groups are also characterized.

We give a method for efficiently computing isomorphisms between towers of Artin-Schreier extensions over a finite field. We find that isomorphisms between towers of degree pn over a fixed field Fq can be computed, composed, and inverted in time essentially linear in pn. The method relies on an approximation process.

We discuss an example of a triangulated Hopf category related to SL(2). It is an equivariant derived category equipped with multiplication and comultiplication functors and structure isomorphisms. We prove some coherence equations for structure isomorphisms. In particular, the Hopf category is monoidal.

The study of isomorphisms of types has been mainly carried out in an intuitionistic setting. We extend some of these works to classical logic for both call-by-name and call-by-value computations by means of polarized linear logic and game semantics. This leads to equational characterizations of these isomorphisms for all the propositional connectives.

It is shown that every  almost linear bijection $h : Arightarrow B$ of a unital $C^*$-algebra $A$ onto a unital$C^*$-algebra $B$ is a $C^*$-algebra isomorphism when $h(3^n u y) = h(3^n u) h(y)$ for allunitaries  $u in A$, all $y in A$, and all $nin mathbb Z$, andthat almost linear continuous bijection $h : A rightarrow B$ of aunital $C^*$-algebra $A$ of real rank zero onto a unital$C^*$-algebra...

We establish isomorphisms between certain specializations of BMW algebras and the symmetric squares of TemperleyLieb algebras. These isomorphisms imply a link-polynomial identity due to W. B. R. Lickorish. As an application, we compute the closed images of the irreducible braid group representations factoring over these specialized BMW algebras.

Let V = B(H) or S(H), where B(H) is the algebra of bounded linear operator acting on the Hilbert space H, and S(H) is the set of self-adjoint operators in B(H). Denote the numerical range of A ∈ B(H) by W (A) = {(Ax, x) : x ∈ H, (x, x) = 1}. It is shown that a surjective map φ : V→ V satisfies W (AB +BA) =W (φ(A)φ(B) + φ(B)φ(A)) for all A,B ∈ V if and only if there is a unitary operator U ∈ B(H...

We study isomorphisms of types in the system of simply-typed λ-calculus with inductive types and recursion. It is shown that in some cases (multiproducts, copies of types), it is possible to add new reductions in such a way that strong normalisation and confluence of the calculus is preserved, and the isomorphisms may be regarded as intensional w.r.t. a stronger equality relation.

The aim of this article is to introduce a new class SO(2)equivariant transversal maps T R(cl(Ω), ∂Ω) and to define degree theory for such maps. We define degree for SO(2)-equivariant transversal maps and prove some properties of this invariant. Moreover, we characterize SO(2)-equivariant transversal isomorphisms and derive formula for degree of such isomorphisms.