We consider a twisted action of a discrete group G on a unital C*-algebra A and give conditions e... more We consider a twisted action of a discrete group G on a unital C*-algebra A and give conditions ensuring that there is a bijective correspondence between the maximal invariant ideals of A and the maximal ideals in the associated reduced C*-crossed product.
Rendiconti del Seminario Matematico e Fisico di Milano, 1982
SuntoSi considerano problemi di controllabilità periodica per processi lineari autonomi in spazi ... more SuntoSi considerano problemi di controllabilità periodica per processi lineari autonomi in spazi di dimensione finita o infinita.SummarySome problems connected with periodic controllability of a linear autonomous process are considered, both in finite and infinite dimensions.
We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely... more We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of MASAa in On. In particular, we exhibit an uncountable family of MASAs, conjugate to the standard MASA Dn via Bogolubov automorphisms, that are not inner conjugate to Dn.
In the context of Connes’ spectral triples, a suitable notio n of morphism is introduced. Discret... more In the context of Connes’ spectral triples, a suitable notio n of morphism is introduced. Discrete groups with length function provide a natur al example for our definitions. Connes’ construction of spectral triples for gro up algebras is a covariant functor from the category of discrete groups with length fun ctions to that of spectral triples. Several interesting lines for future study of the categorical properties of spectral triples and their variants are suggested.
Every unitary solution of the Yang-Baxter equation (R-matrix) in dimension $d$ can be viewed as a... more Every unitary solution of the Yang-Baxter equation (R-matrix) in dimension $d$ can be viewed as a unitary element of the Cuntz algebra ${\mathcal O}_d$ and as such defines an endomorphism of ${\mathcal O}_d$. These Yang-Baxter endomorphisms restrict and extend to endomorphisms of several other $C^*$- and von Neumann algebras and furthermore define a II$_1$ factor associated with an extremal character of the infinite braid group. This paper is devoted to a detailed study of such Yang-Baxter endomorphisms. Among the topics discussed are characterizations of Yang-Baxter endomorphisms and the relative commutants of the various subfactors they induce, an endomorphism perspective on algebraic operations on R-matrices such as tensor products and cabling powers, and properties of characters of the infinite braid group defined by R-matrices. In particular, it is proven that the partial trace of an R-matrix is an invariant for its character by a commuting square argument. Yang-Baxter endomorp...
After recalling in detail some basic definitions on Hilbert C*-bimodules, Morita equivalence and ... more After recalling in detail some basic definitions on Hilbert C*-bimodules, Morita equivalence and imprimitivity, we discuss a spectral reconstruction theorem for imprimitivity Hilbert C*-bimodules over commutative unital C*-algebras and consider some of its applications in the theory of commutative full C*-categories.
Given a completely rational conformal net A on S, its fusion ring acts faithfully on the K-group ... more Given a completely rational conformal net A on S, its fusion ring acts faithfully on the K-group K0(KA) of a certain universal C*-algebra KA associated to A, as shown in a previous paper. We prove here that this action can actually be identified with a Kasparov product, thus paving the way for a fruitful interplay between conformal field theory and KK-theory.
We consider a twisted action of a discrete group G on a unital C*-algebra A and give conditions e... more We consider a twisted action of a discrete group G on a unital C*-algebra A and give conditions ensuring that there is a bijective correspondence between the maximal invariant ideals of A and the maximal ideals in the associated reduced C*-crossed product.
Rendiconti del Seminario Matematico e Fisico di Milano, 1982
SuntoSi considerano problemi di controllabilità periodica per processi lineari autonomi in spazi ... more SuntoSi considerano problemi di controllabilità periodica per processi lineari autonomi in spazi di dimensione finita o infinita.SummarySome problems connected with periodic controllability of a linear autonomous process are considered, both in finite and infinite dimensions.
We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely... more We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of MASAa in On. In particular, we exhibit an uncountable family of MASAs, conjugate to the standard MASA Dn via Bogolubov automorphisms, that are not inner conjugate to Dn.
In the context of Connes’ spectral triples, a suitable notio n of morphism is introduced. Discret... more In the context of Connes’ spectral triples, a suitable notio n of morphism is introduced. Discrete groups with length function provide a natur al example for our definitions. Connes’ construction of spectral triples for gro up algebras is a covariant functor from the category of discrete groups with length fun ctions to that of spectral triples. Several interesting lines for future study of the categorical properties of spectral triples and their variants are suggested.
Every unitary solution of the Yang-Baxter equation (R-matrix) in dimension $d$ can be viewed as a... more Every unitary solution of the Yang-Baxter equation (R-matrix) in dimension $d$ can be viewed as a unitary element of the Cuntz algebra ${\mathcal O}_d$ and as such defines an endomorphism of ${\mathcal O}_d$. These Yang-Baxter endomorphisms restrict and extend to endomorphisms of several other $C^*$- and von Neumann algebras and furthermore define a II$_1$ factor associated with an extremal character of the infinite braid group. This paper is devoted to a detailed study of such Yang-Baxter endomorphisms. Among the topics discussed are characterizations of Yang-Baxter endomorphisms and the relative commutants of the various subfactors they induce, an endomorphism perspective on algebraic operations on R-matrices such as tensor products and cabling powers, and properties of characters of the infinite braid group defined by R-matrices. In particular, it is proven that the partial trace of an R-matrix is an invariant for its character by a commuting square argument. Yang-Baxter endomorp...
After recalling in detail some basic definitions on Hilbert C*-bimodules, Morita equivalence and ... more After recalling in detail some basic definitions on Hilbert C*-bimodules, Morita equivalence and imprimitivity, we discuss a spectral reconstruction theorem for imprimitivity Hilbert C*-bimodules over commutative unital C*-algebras and consider some of its applications in the theory of commutative full C*-categories.
Given a completely rational conformal net A on S, its fusion ring acts faithfully on the K-group ... more Given a completely rational conformal net A on S, its fusion ring acts faithfully on the K-group K0(KA) of a certain universal C*-algebra KA associated to A, as shown in a previous paper. We prove here that this action can actually be identified with a Kasparov product, thus paving the way for a fruitful interplay between conformal field theory and KK-theory.
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