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Operator algebra

About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.


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TL;DR: In this article, the existence of conditional expectation preserving embeddings of C$^*-algebras was shown for certain classes of unital completely positive maps under conditional expectation-preserving embedding.
Abstract: Given reduced amalgamated free products of C$^*$-algebras, $(A,phi)=*_i(A_i,phi_i)$ and $(D,psi)=*_i(D_i,psi_i)$, an embedding $A\to D$ is shown to exist assuming there are conditional expectation preserving embeddings $A_i\to D_i$. This result is extended to show the existance of the reduced amalgamated free product of certain classes of unital completely positive maps. Analogues of the above mentioned results are proved for von Neumann algebras.

53 citations

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TL;DR: In this article, a U(N)-invariant Hamiltonian operator for spin networks is proposed and the authors explore the analogies between this model and loop quantum cosmology and sketch some possible generalizations of it.
Abstract: We use the recently introduced U(N) framework for loop quantum gravity to study the dynamics of spin network states on the simplest class of graphs: two vertices linked with an arbitrary number N of edges. Such graphs represent two regions, in and out, separated by a boundary surface. We study the algebraic structure of the Hilbert space of spin networks from the U(N) perspective. In particular, we describe the algebra of operators acting on that space and discuss their relation to the standard holonomy operator of loop quantum gravity. Furthermore, we show that it is possible to make the restriction to the isotropic/homogeneous sector of the model by imposing the invariance under a global U(N) symmetry. We then propose a U(N)-invariant Hamiltonian operator and study the induced dynamics. Finally, we explore the analogies between this model and loop quantum cosmology and sketch some possible generalizations of it.

53 citations

Posted Content
TL;DR: In this paper, the authors studied the effect of the bulk deformations on the algebra of boundary operators, which is a homotopy Lie algebra, which can be understood in terms of a closed string field theory.
Abstract: We study topological open membranes of BF type in a manifest BV formalism. Our main interest is the effect of the bulk deformations on the algebra of boundary operators. This forms a homotopy Lie algebra, which can be understood in terms of a closed string field theory. The simplest models are associated to quasi-Lie bialgebras and are of Chern-Simons type. More generally, the induced structure is a Courant algebroid, or ``quasi-Lie bialgebroid'', with boundary conditions related to Dirac bundles. A canonical example is the topological open membrane coupling to a closed 3-form, modeling the deformation of strings by a C-field. The Courant algebroid for this model describes a modification of deformation quantization. We propose our models as a tool to find a formal solution to the quantization problem of Courant algebroids.

53 citations

Posted Content
TL;DR: In this article, a new proof of Kirchberg's theorem on the tensor product of B(H) with the group C*-algebra of a countable free group is given, and an affirmative solution to the Connes embedding problem is implied by various matrix-theoretic problems.
Abstract: An operator system modulo the kernel of a completely positive linear map of the operator system gives rise to an operator system quotient. In this paper, operator system quotients and quotient maps of certain matrix algebras are considered. Some applications to operator algebra theory are given, including a new proof of Kirchberg's theorem on the tensor product of B(H) with the group C*-algebra of a countable free group. We also show that an affirmative solution to the Connes Embedding Problem is implied by various matrix-theoretic problems, and we give a new characterisation of unital C*-algebras that have the weak expectation property.

53 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202337
202277
2021125
2020141
2019173
2018169