Extending Pirashvili’s work, we characterize small additive categories A such that the inclusion in the category of functors from A to abelian groups of the full subcategory of analytic functors induces an isomorphism between extension groups.

Mathieu and Ruddy proved that if be a unital spectral isometry from a unital C*-algebra Aonto a unital type I C*-algebra B whose primitive ideal space is Hausdorff and totallydisconnected, then is Jordan isomorphism. The aim of this note is to show that if be asurjective spectrum preserving additive map, then is a Jordan isomorphism without the extraassumption totally disconnected.

We consider two categories of C-algebras; in the first, the isomorphisms are ordinary isomorphisms, and in the second, the isomorphisms are Morita equivalences. We show how these two categories, and categories of dynamical systems based on them, crop up in a variety of C-algebraic contexts. We show that Rieffel’s construction of a fixed-point algebra for a proper action can be made into functor...

(In first case we say (F,G2) are an adjoint pair and in the second case we say that (G1, F ) are an adjoint pair.) (2) An object A in a category C is called initial (resp. final) if for every object B in C, HomC(A,B) (resp. HomC(B,A)) is a singleton. Prove that an initial (resp. final) object, if it exists, is unique up to unique isomorphism. Determine if such objects exist in the following cat...

In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.

It is well known that a measured groupoid G defines a von Neu-mann algebra W * (G), and that a Lie groupoid G canonically defines both a C *-algebra C * (G) and a Poisson manifold A * (G). We show that the maps (G) are functorial with respect to suitable categories. In these categories Morita equivalence is isomorphism of objects, so that these maps preserve Morita equivalence.

In this paper, using generating functions we study two categories E and C of modules for twisted affine Lie algebras ĝ[σ], which were firstly introduced and studied in [Li] for untwisted affine Lie algebras. We classify integrable irreducible ĝ[σ]-modules in categories E and C, where E is proved to contain the well known evaluation modules and C to unify highest weight modules, evaluation modul...

Working jointly in the equivalent categories of MV-algebras and lattice-ordered abelian groups with strong order unit (for short, unital l-groups), we prove that isomorphism is a sufficient condition for a separating subalgebra A of a finitely presented algebra F to coincide with F . The separation and isomorphism conditions do not individually imply A = F . Various related problems, like the s...