Topic
Operator algebra
About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.
Papers published on a yearly basis
Papers
More filters
27 Nov 2001
TL;DR: In this article, the DR-duality theory for compact groups is applied to endomorphism categories of C*-algebras with nontrivial center by H. Evans.
Abstract: An application of the DR-duality theory for compact groups to endomorphism categories of C*-algebras with nontrivial center by H. Baumgartel and F. Lledo Modular invariants and subfactors by J. Bockenhauer and D. E. Evans On the PCT-theorem in the theory of local observables by H. J. Borchers and J. Yngvason Transplantation of local nets and geometric modular action on Robertson-Walker space-times by D. Buchholz, J. Mund, and S. J. Summers Classification of subsystems, local symmetry generators and intrinsic definition of local observables by S. Carpi and R. Conti From local perturbation theory to Hopf- and Lie-algebras of Feynman graphs by A. Connes and D. Kreimer The flat tube theorem for vector valued functions by C. D'Antoni and L. Zsido Point interactions by G. Dell'Antonio Perturbative algebraic field theory, and deformation quantization by M. Dutsch and K. Fredenhagen Sum rules for the free energy in the mean field spin glass model by F. Guerra Fractals in noncommutative geometry by D. Guido and T. Isola What I woud like to understand by R. Haag The Rohlin property for automorphisms of $C^*$-algebras by M. Izumi Environment induced localization and superselection rules in a gas of pyramidal molecules by G. Jana-Lasinio, C. Presilla, and C. Toninelli Connes-Moscovici-Kreimer Hopf algebras by D. Kastler The structure of the automorhpism group of an approximately finite dimensional factor by Y. Katayama and M. Takesaki Braiding and extensions of endomrophisms of subfactors by Y. Kawahigashi Bicategories of operator algebras and Poisson manifolds by N. P. Landsman Notes for a quantum index theorem introduction by R. Longo Conformal field theory and Doplicher-Roberts reconstruction by M. Muger On the distance between MASA's in type II$_1$ factors by S. Popa Recent results concerning E$_o$-semigroups of $\mathfrak{B}(\mathfrak{H})$ by R. T. Powers Locality and modular invariance in 2D conformal QFT by K.-H. Rehren Tensor products of Banach spaces and the Stone-Weierstrass problem of $C^*$-algebras by S. Sakai Perron-Frobenius theory for positive maps on trace ideals by R. Schrader Space- and time-like superselection rules in conformal quantum field theory by B. Schroer Finite quantum groupoids and inclusions of finite type by K. Szlachanyi On generalizations of the spectrum condition by R. Verch Algebraic orbifold conformal field theories by F. Xu.
40 citations
TL;DR: In this paper, the supremum of the norm of RA,B(X) over all unit rank one operators on E is characterized, and the lower estimate d(LA−RB) is shown to be ⩾max{supλ∈V(B)∥A∥+∥B∥} (where V is the algebraic range of X in A ).
40 citations
Posted Content•
TL;DR: In this article, the intersection cohomology of certain moduli spaces ("framed Uhlenbeck spaces") together with some structures on them (such as e.g. the Poincare pairing) is described in terms of representation theory of some vertex operator algebras.
Abstract: We describe the (equivariant) intersection cohomology of certain moduli spaces ("framed Uhlenbeck spaces") together with some structures on them (such as e.g.\ the Poincare pairing) in terms of representation theory of some vertex operator algebras ("$\mathscr W$-algebras").
40 citations
TL;DR: In this article, the authors give a brief introduction to Conformal Field Theory (CFT) following the presentation of G Segal and explain how to reconstruct part of a CFT from its fusion rules.
Abstract: In this paper, we give a brief introduction to Conformal Field Theory (CFT) following the presentation of G Segal We explain how to reconstruct part of a CFT from its fusion rules The possible choices of S matrices are indexed by some automorphisms of the fusion algebra We illustrate this procedure by computing the modular properties of the possible genus-one characters when the fusion algebra is the representation algebra of a finite group We also classify the modular invariant partition functions of these theories We recover as special cases the A N (1) WZW theories and the rational gaussian model
40 citations
[...]
TL;DR: In this article, the authors associate vertex operator algebras to web of interfaces in the topologically twisted super Yang-Mills theory, and propose a BRST construction of the vertex operators and check in examples that both constructions agree.
Abstract: We associate vertex operator algebras to $(p,q)$-webs of interfaces in the topologically twisted $\mathcal{N}=4$ super Yang-Mills theory. Y-algebras associated to trivalent junctions are identified with truncations of $\mathcal{W}_{1+\infty}$ algebra. Starting with Y-algebras as atomic elements, we describe gluing of Y-algebras analogous to that of the topological vertex. At the level of characters, the construction matches the one of counting D0-D2-D4 bound states in toric Calabi-Yau threefolds. For some configurations of interfaces, we propose a BRST construction of the algebras and check in examples that both constructions agree. We define generalizations of $\mathcal{W}_{1+\infty}$ algebra and identify a large class of glued algebras with their truncations. The gluing construction sheds new light on the structure of vertex operator algebras conventionally constructed by BRST reductions or coset constructions and provides us with a way to construct new algebras. Many well-known vertex operator algebras, such as $U(N)_k$ affine Lie algebra, $\mathcal{N}=2$ superconformal algebra, $\mathcal{N}=2$ super-$\mathcal{W}_\infty$, Bershadsky-Polyakov $\mathcal{W}_3^{(2)}$, cosets and Drinfeld-Sokolov reductions of unitary groups can be obtained as special cases of this construction.
40 citations