Related papers: Transferring homotopy commutative algebraic struct…

In this article, we study the permanence of topological and algebraic dimension type properties of simple unital $C\sp*$-algebras. When a pair of unital $C\sp*$-algebras $(A, B)$ is associated by a $*$-homomorphism $\phi: A\to B$ which is…

We define the concept of a partial translation structure T on a metric space X and we show that there is a natural C*-algebra C*(T) associated with it which is a subalgebra of the uniform Roe algebra C*_u(X). We introduce a coarse invariant…

We construct an explicit minimal model for an algebra over the cobar-construction of a differential graded operad. The structure maps of this minimal model are expressed in terms of sums over decorated trees. We introduce the appropriate…

There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…

We prove that every surjective unital linear mapping which preserves invertible elements from a Banach algebra onto a C*-algebra carrying a faithful tracial state is a Jordan homomorphism thus generalising Aupetit's 1998 result for finite…

Let $A$ and $C$ be two unital simple C*-algebas with tracial rank zero. Suppose that $C$ is amenable and satisfies the Universal Coefficient Theorem. Denote by ${{KK}}_e(C,A)^{++}$ the set of those $\kappa$ for which…

We give a new short proof that the wheeled operad of unimodular Lie algebras is Koszul and use this to explicitly construct its minimal resolution. A representation of this resolution in a finite dimensional vector space V we call a…

We complete the details of a theory outlined by Kontsevich and Soibelman that associates to a semi-algebraic set a certain graded commutative differential algebra of "semi-algebraic differential forms" in a functorial way. This algebra…

We study actions of ``compact quantum groups'' on ``finite quantum spaces''. According to Woronowicz and to general $\c^*$-algebra philosophy these correspond to certain coactions $v:A\to A\otimes H$. Here $A$ is a finite dimensional…

We consider the functor C that to a unital C*-algebra A assigns the partial order set C(A) of its commutative C*-subalgebras ordered by inclusion. We investigate how some C*-algebraic properties translate under the action of C to…

We use compactifications of C*-algebras to introduce noncommutative coarse geometry. We transfer a noncommutative coarse structure on a C*-algebra with an action of a locally compact Abelian group by translations to Rieffel deformations and…

Starting from an arbitrary endomorphism $\alpha$ of a unital C*-algebra $A$ we construct a bigger C*-algebra $B$ and extend $\alpha$ onto $B$ in such a way that the extended endomorphism $\alpha$ has a unital kernel and a hereditary range,…

Universal continuous calculi are defined and it is shown that for every finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an ordered *-algebra that is symmetric, i.e. "strictly" positive elements are invertible, and…

The perturbation lemma and the homotopy transfer for L-infinity algebras is proved in a elementary way by using a relative version of the ordinary perturbation lemma for chain complexes and the coalgebra perturbation lemma.

We solve a class of lifting problems involving approximate polynomial relations (soft polynomial relations). Various associated C*-algebras are therefore projective. The technical lemma we need is a new manifestation of Akemann and…

We show that the canonical map from the associative operad to the unital associative operad is a homotopy epimorphism for a wide class of symmetric monoidal model categories. As a consequence, the space of unital associative algebra…

We study a tracial notion of Z-absorption for simple, unital C*-algebras. We show that if A is a C*-algebra for which this property holds then A has almost unperforated Cuntz semigroup, and if in addition A is nuclear and separable we show…

We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more…

In this paper, we extend the Banach-Stone theorem to the non commutative case, i.e, we prove that the structure of the liminal $C^{*}$-algebras $\cal A$ determines the topology of its primitive ideal space.

Let E be a row-finite directed graph. We prove that there exists a C*-algebra C*_{min}(E) with the following co-universal property: given any C*-algebra B generated by a Toeplitz-Cuntz-Krieger E-family in which all the vertex projections…