Related papers: Morita Type Equivalences and Reflexive Algebras

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…

We prove that two unital dual operator algebras A, B are stably isomorphic if and only if they are Delta-equivalent, if and only if they have completely isometric normal representations a, b on Hilbert spaces H, K respectively and there…

We study the *-double functor between the categories of associative and involutive algebras. It is proved that an associative algebra is isomorphic to a subalgebra of a $C\sp*$-algebra if and only if its *-double is *-isomorphic to a…

Let $\delta(\mathcal{P})$ be the $\delta$-vector of a reflexive polytope $\mathcal{P} \subset \mathbb{R}^d$ of dimension $d$ and $\delta(\mathcal{P} ^\vee)$ the $\delta$-vector of the dual polytope $\mathcal{P}^\vee \subset \mathbb{R}^d$.…

If C and D are varieties of algebras in the sense of general algebra, then by a representable functor C --> D we understand a functor which, when composed with the forgetful functor D --> Set, gives a representable functor in the classical…

We construct a functor that maps $C^*$-correspondences to their Cuntz-Pimsner algebras. The objects in our domain category are $C^*$-correspondences, and the morphisms are the isomorphism classes of $C^*$-correspondences satisfying certain…

We consider two inclusions of $C^*$-algebras whose small $C^*$-algebras have approximate units of the large $C^*$-algebras and their two spaces of all bounded bimodule linear maps. We suppose that the two inclusions of $C^*$-algebras are…

We give a category theoretic approach to several known equivalences from (classic) tilting theory and commutative algebra. Furthermore, we apply our main results to establish a duality theory for relative Cohen-Macaulay modules in the sense…

A bivariant functor is defined on a category of *-algebras and a category of operator ideals, both with actions of a second countable group $G$, into the category of abelian monoids. The element of the bivariant functor will be…

Given C*-algebras A and B and an imprimitivity A-B-bimodule X, we construct an explicit isomorphism X_* : K_i(A) --> K_i(B) where K_i denote the complex K-theory functors for i=0, 1. Our techniques do not require separability nor existence…

Two rings A and B are said to be derived Morita equivalent if their derived categories of modules are equivalent. By results of Rickard, if A and B are derived Morita equivalent algebras over a field k, then there is a complex of bimodules…

We will introduce the notion of strong Morita equivalence for completely positive linear maps and study its basic properties. Also, we will discuss the relation between strong Morita equivalence for bounded $C^*$-bimodule linear maps and…

We develop Tannaka duality theory for dg categories. To any dg functor from a dg category $\mathcal{A}$ to finite-dimensional complexes, we associate a dg coalgebra $C$ via a Hochschild homology construction. When the dg functor is…

In previous work, we defined and studied $\Sigma^*$-modules, a class of Hilbert $C^*$-modules over $\Sigma^*$-algebras (the latter are $C^*$-algebras that are sequentially closed in the weak operator topology). The present work continues…

In this paper, we try to answer the following question: given a modular tensor category $\A$ with an action of a compact group $G$, is it possible to describe in a suitable sense the ``quotient'' category $\A/G$? We give a full answer in…

A new class of locally unital and locally finite dimensional algebras $A$ over an arbitrary algebraically closed field is discovered. Each of them admits an upper finite weakly triangular decomposition, a generalization of an upper finite…

Let N_1 (resp.N_2) be a nest A (resp. B) be the corresponding nest algebra, A_0 (resp. B_0) be the subalgebra of compact operators. We prove that the nests N_1, N_2 are isomorphic if and only if the algebras A, B are weakly-* Morita…

We show that there is a functor from the category of positive admissible ternary rings to the category of $*$-algebras, which induces an isomorphism of partially ordered sets between the families of $C^*$-norms on the ternary ring and its…

$\DeclareMathOperator{\G}{\mathbb{G}}\DeclareMathOperator{\Rep}{Rep} \DeclareMathOperator{\Corr}{Corr}$Let $\G$ be a locally compact quantum group and $(M, \alpha)$ a $\G$-$W^*$-algebra. The object of study of this paper is the…

A modular fusion category C allows one to define projective representations of the mapping class groups of closed surfaces of any genus. We show that if all these representations are irreducible, then C has a unique Morita-class of simple…