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101.
We canonically associate to any planar algebra two type II∞ factors M±. The subfactors constructed previously by the authors in Guionnet et al. (2010) [6] are isomorphic to compressions of M± to finite projections. We show that each M± is isomorphic to an amalgamated free product of type I von Neumann algebras with amalgamation over a fixed discrete type I von Neumann subalgebra. In the finite-depth case, existing results in the literature imply that M+≅M− is the amplification a free group factor on a finite number of generators. As an application, we show that the factors Mj constructed in Guionnet et al. (in press) [6] are isomorphic to interpolated free group factors L(F(rj)), rj=1+2δ−2j(δ−1)I, where δ2 is the index of the planar algebra and I is its global index. Other applications include computations of laws of Jones-Wenzl projections. 相似文献
102.
Let T be a Cowen-Douglas operator. In this paper, we study the von Neumann algebra V?(T) consisting of operators commuting with both T and T? from a geometric viewpoint. We identify operators in V?(T) with connection-preserving bundle maps on E(T), the holomorphic Hermitian vector bundle associated to T. By studying such bundle maps, the structure of V?(T) as well as information on reducing subspaces of T can be determined. 相似文献
103.
Liviu P?unescu 《Journal of Functional Analysis》2011,261(9):2461-2485
The notion of sofic equivalence relation was introduced by Gabor Elek and Gabor Lippner. Their technics employ some graph theory. Here we define this notion in a more operator algebraic context, starting from Connes? Embedding Problem, and prove the equivalence of these two definitions. We introduce a notion of sofic action for an arbitrary group and prove that an amalgamated product of sofic actions over amenable groups is again sofic. We also prove that an amalgamated product of sofic groups over an amenable subgroup is again sofic. 相似文献
104.
J. Cimpri? 《Journal of Functional Analysis》2011,260(10):3132-3145
We prove a general archimedean positivstellensatz for hermitian operator-valued polynomials and show that it implies the multivariate Fejer-Riesz theorem of Dritschel-Rovnyak and positivstellensätze of Ambrozie-Vasilescu and Scherer-Hol. We also obtain several generalizations of these and related results. The proof of the main result depends on an extension of the abstract archimedean positivstellensatz for ?-algebras that is interesting in its own right. 相似文献
105.
106.
Mohamed M.S. Nasser 《Journal of Mathematical Analysis and Applications》2011,382(1):47-56
This paper presents a boundary integral method for approximating the conformal mappings from any bounded or unbounded multiply connected region G onto the second, third and fourth categories of Koebe?s canonical slit domains. The method can be also used for calculating the conformal mappings of simply and doubly connected regions. The method is an extension of the author?s method for the first category of Koebe?s canonical slit domains (see [M.M.S. Nasser, Numerical conformal mapping via a boundary integral equation with the generalized Neumann kernel, SIAM J. Sci. Comput. 31 (2009) 1695-1715]). Three numerical examples are presented to illustrate the performance of the proposed method. 相似文献
107.
非交换的Poisson代数同时具有(未必交换的)结合代数和李代数两种代数结构,且结合代数和李代数之间满足所谓的Leibniz法则.本文确定了一般广义仿射李代数上所有的Poisson代数结构. 相似文献
108.
109.
Let H be a finite-dimensional weak Hopf algebra and A a left H-module algebra with its invariant subalgebra A~H.We prove that the smash product A#H is an A-ring with a grouplike character, and give a criterion for A#H to be Frobenius over A. Using the theory of A-rings, we mainly construct a Morita context connecting the smash product A#H and the invariant subalgebra A~H , which generalizes the corresponding results obtained by Cohen, Fischman and Montgomery. 相似文献
110.
We investigate the Morita context and graded cases for weak group corings and derive some equivalent conditions for μ to be
surjective. Furthermore, we develop Galois theory for weak group corings. As an application, we give Galois theory for comodulelike
algebras over a weak Hopf group coalgebra. 相似文献