相关论文: The homotopy lifting theorem for semiprojective C*…

The equivariant version of semiprojectivity was recently introduced by the first author. We study properties of this notion, in particular its relation to ordinary semiprojectivity of the crossed product and of the algebra itself. We show…

We construct uncountably many mutually nonisomorphic simple separable stably finite unital exact C$^\ast$-algebras which are not isomorphic to their opposite algebras. In particular, we prove that there are uncountably many possibilities…

We consider a class of extensions of associative algebras, which we refer to as ``strongly proj-bounded extensions''. We prove that the finiteness of the left global dimension and the support of the Hochschild homology is preserved by…

In this paper we consider certain proejctions in the corona algebra of $C(X)\otimes B$ associated to $(p_0, p_1, \dots, p_n)$ where $p_i: X_i \to \mt_s$ a continuous projection valued section to the multiplier algebra of a stable…

A C*-metric algebra consists of a unital C*-algebra and a Leibniz Lip-norm on the C*-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital *-homomorphism from a C*-metric algebra to another one is…

We show that ||u*u - v*v|| \leq ||u - v|| for partial isometries u and v. There is a stronger inequality if both u and v are extreme points of the unit ball of a C*-algebra, and both inequalities are sharp. If u and v are partial isometries…

We prove that a unital completely positive map between finite-dimensional C*-algebras is a homomorphism if and only if it is completely entropy-nonincreasing, where the relevant notion of entropy is a variant of von Neumann entropy. This…

Nuclear C*-algebras enjoy a number of approximation properties, most famously the completely positive approximation property. This was recently sharpened to arrange for the incoming maps to be sums of order-zero maps. We show that, in…

We provide the rigorous foundations for a categorical approach to the classification of C*-dynamics up to cocycle conjugacy. Given a locally compact group $G$, we consider a category of (twisted) $G$-C*-algebras, where morphisms between two…

We study cohomology theories of strongly homotopy algebras, namely $A_\infty, C_\infty$ and $L_\infty$-algebras and establish the Hodge decomposition of Hochschild and cyclic cohomology of $C_\infty$-algebras thus generalising previous work…

We give a new definition of the semigroup C*-algebra of a left cancellative semigroup, which resolves problems of the construction by X. Li. Namely, the new construction is functorial, and the independence of ideals in the semigroup does…

For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative…

For all classical groups (and for their analogs in infinite dimension or over general base fields or rings) we construct certain contractions, called "homotopes". The construction is geometric, using as ingredient involutions of associative…

Motivated by algebraic quantum field theory and our previous work we study properties of inductive systems of \ $C^*$-algebras over arbitrary partially ordered sets. A partially ordered set can be represented as the union of the family of…

Let $A$ be a separable amenable $C^*$-algebra and $B$ a non-unital and $\sigma$-unital simple $C^*$-algebra with continuous scale ($B$ need not be stable). We classify, up to unitary equivalence, all essential extensions of the form $0…

In this paper we continue the analysis undertaken in a series of previous papers on structures arising as completions of C*-algebras under topologies coarser that their norm and we focus our attention on the so-called {\em locally convex…

We give a sufficient condition for a $^*$-algebra with a specified basis to have an enveloping $C^*$-algebra. Particularizing to the setting of a Hecke algebra $\h(G,\gm)$, we show that under a suitable assumption not only we can assure…

We introduce a notion of ellipticity of complexes of linear pseudodifferential operators acting on sections of $A$-Hilbert bundles over smooth manifolds, $A$ being a $C^*$-algebra. We prove that the cohomology groups of an $A$-elliptic…

In this paper, we introduce homological structure theory of semirings and CP-semirings---semirings all of whose cyclic semimodules are projective. We completely describe semisimple, Gelfand, subtractive, and anti-bounded, CP-semirings. We…

This survey article on relative homological algebra in bivariant K-thoery is mainly intended for readers with a background knowledge in triangulated categories. We briefly recall the general theory of relative homological algebra in…