The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

These rings admit numerous algebraic and geometric realizations, but one of the historically first constructions, dating to the work of Steinitz in 1900 completed later by Hall, was given in terms of what is now called the classical Hall algebra H (see [Ma], Chapter II ). This algebra has a basis consisting of isomorphism classes of abelian q-groups, where q is a fixed prime power, and the stru...

Let be a nite dimensional hereditary algebra over a nite eld k; H(() and C(() be respectively the Hall algebra and the composition algebra of ; P be the isomorphism classes of nite dimensional-modules and I the isomorphism classes of simple-modules. We deene and , 2 P, to be the right and left derivations of H(() respectively. By using these derivations and the action of the braid group on the ...

A C∞-Hopf algebra is a C∞-algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those C∞-Hopf algebras which are given by the algebra C∞(G) of smooth functions on some compact Lie group G, thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.

Following E. Kirchberg, [3], we call a bifunctor (A,B) → A⊗α B a C -algebraic tensor product functor if it is obtained by completing of the algebraic tensor product A ⊙ B of C-algebras in a functional way with respect to a suitable C-norm ‖ · ‖α. We call such a functor symmetric if the standard isomorphism A ⊙ B ∼= B ⊙ A extends to an isomorphism A⊗αB ∼= B⊗αA. Similarly, we call it associative ...

We consider the algebra isomorphism found by Frenkel and Ding between the RLL and the Drinfeld realizations of Uq(ĝl(2)). After we note that this is not a Hopf algebra isomorphism, we prove that there is a unique Hopf algebra structure for the Drinfeld realization so that this isomorphism becomes a Hopf algebra isomorphism. Though more complicated, this Hopf algebra structure is also closed, ju...

In this note, unless we say otherwise every vector space or algebra we speak about is over C. If A is a Banach algebra and e ∈ A satisfies xe = x and ex = x for all x ∈ A, and also ‖e‖ = 1, we say that e is unity and that A is unital. If A is a unital Banach algebra and x ∈ A, the spectrum of x is the set σ(x) of those λ ∈ C for which λe−x is not invertible. It is a fact that if A is a unital B...

Classification theory guarantees the existence of an isomorphism between any two E8’s, at least over an algebraically closed field of characteristic 0. The purpose of this paper is to construct for any Jordan algebra J of degree 3 over a field Φ of characteristic ≠ 2,3 an explicit isomorphism between the algebra obtained from J by Faulkner’s construction and the algebra obtained from the split ...

Abstract Let G be a finite group, let A an infinite-dimensional stably simple unital C*-algebra, and $\alpha \colon \to {\operatorname {Aut}} (A)$ action of on which has the weak tracial Rokhlin property. $A^{\alpha }$ fixed point algebra. Then radius comparison satisfies ${\operatorname {rc}} (A^{\alpha }) \leq ( C^* (G, A, \alpha ) ({1}/{{{\operatorname{card}}} (G))} \cdot . The inclusion in ...

In this paper, we study a family of C*-subalgebras defined by fixed points generalized gauge actions Cuntz–Krieger algebra introducing étale groupoids whose associated C*-algebras are these C*-subalgebras. We show that topological conjugacy classes one-sided Markov shifts characterized in terms the isomorphism groupoids.