The Experts below are selected from a list of 9 Experts worldwide ranked by ideXlab platform

David R Pitts - One of the best experts on this subject based on the ideXlab platform.

  • the algebraic structure of non commutative analytic toeplitz algebras
    Mathematische Annalen, 1998
    Co-Authors: Kenneth R Davidson, David R Pitts
    Abstract:

    The non-commutative analytic Toeplitz algebra is the wot– closed algebra generated by the left regular representation of the free semigroup on n generators. We develop a detailed picture of the algebraic structure of this algebra. In particular, we show that there is a Canonical homomorphism of the automorphism group onto the group of conformal automorphisms of the complex n-ball. The k-dimensional representations form a generalized maximal ideal space with a Canonical Surjection onto the ball of k × kn matrices which is a homeomorphism over the open ball analogous to the fibration of the maximal ideal space of H∞ over the unit disk. In [6, 17, 18, 20], a good case is made that the appropriate analogue for the analytic Toeplitz algebra in n non-commuting variables is the wotclosed algebra generated by the left regular representation of the free semigroup on n generators. The papers cited obtain a compelling analogue of Beurling’s theorem and inner–outer factorization. In this paper, we add further evidence. The main result is a short exact sequence determined by a Canonical homomorphism of the automorphism group onto this algebra onto the group of conformal automorphisms of the unit ball of Cn. The kernel is the subgroup of quasi-inner automorphisms, which are trivial modulo the wot-closed commutator ideal. Additional evidence of analytic properties comes from the structure of k-dimensional (completely contractive) representations, which have a structure very similar to the fibration of the maximal ideal space of H∞ over the unit disk. An important tool in our analysis is a detailed structure theory for wot-closed right ideals. Curiously, left ideals remain more obscure. The non-commutative analytic Toeplitz algebra Ln is determined by the left regular representation of the free semigroup Fn on n generators z1, . . . , zn which acts on `2(Fn) by λ(w)ξv = ξwv for v, w in Fn. In particular, the algebra Ln is the unital, wot-closed algebra generated by the isometries Li = λ(zi) for 1 ≤ i ≤ n. This algebra and its norm-closed version (the noncommutative disk algebra) were introduced by Popescu [19] in an abstract sense in connection with a non-commutative von Neumann inequality and 1991 Mathematics Subject Classification. 47D25. March 9, 1997; October 9, 1997 final draft. First author partially supported by an NSERC grant and a Killam Research Fellowship. Second author partially supported by an NSF grant.

Kenneth R Davidson - One of the best experts on this subject based on the ideXlab platform.

  • the algebraic structure of non commutative analytic toeplitz algebras
    Mathematische Annalen, 1998
    Co-Authors: Kenneth R Davidson, David R Pitts
    Abstract:

    The non-commutative analytic Toeplitz algebra is the wot– closed algebra generated by the left regular representation of the free semigroup on n generators. We develop a detailed picture of the algebraic structure of this algebra. In particular, we show that there is a Canonical homomorphism of the automorphism group onto the group of conformal automorphisms of the complex n-ball. The k-dimensional representations form a generalized maximal ideal space with a Canonical Surjection onto the ball of k × kn matrices which is a homeomorphism over the open ball analogous to the fibration of the maximal ideal space of H∞ over the unit disk. In [6, 17, 18, 20], a good case is made that the appropriate analogue for the analytic Toeplitz algebra in n non-commuting variables is the wotclosed algebra generated by the left regular representation of the free semigroup on n generators. The papers cited obtain a compelling analogue of Beurling’s theorem and inner–outer factorization. In this paper, we add further evidence. The main result is a short exact sequence determined by a Canonical homomorphism of the automorphism group onto this algebra onto the group of conformal automorphisms of the unit ball of Cn. The kernel is the subgroup of quasi-inner automorphisms, which are trivial modulo the wot-closed commutator ideal. Additional evidence of analytic properties comes from the structure of k-dimensional (completely contractive) representations, which have a structure very similar to the fibration of the maximal ideal space of H∞ over the unit disk. An important tool in our analysis is a detailed structure theory for wot-closed right ideals. Curiously, left ideals remain more obscure. The non-commutative analytic Toeplitz algebra Ln is determined by the left regular representation of the free semigroup Fn on n generators z1, . . . , zn which acts on `2(Fn) by λ(w)ξv = ξwv for v, w in Fn. In particular, the algebra Ln is the unital, wot-closed algebra generated by the isometries Li = λ(zi) for 1 ≤ i ≤ n. This algebra and its norm-closed version (the noncommutative disk algebra) were introduced by Popescu [19] in an abstract sense in connection with a non-commutative von Neumann inequality and 1991 Mathematics Subject Classification. 47D25. March 9, 1997; October 9, 1997 final draft. First author partially supported by an NSERC grant and a Killam Research Fellowship. Second author partially supported by an NSF grant.

Antonio M Cegarra - One of the best experts on this subject based on the ideXlab platform.

  • group theoretic algebraic models for homotopy types
    Journal of Pure and Applied Algebra, 1991
    Co-Authors: P Carrasco, Antonio M Cegarra
    Abstract:

    Abstract In this paper a nonabelian version of the Dold-Kan-Puppe theorem is provided, showing how the Moore-complex functor defines a full equivalence between the category of simplicial groups and the category of what is called ‘hypercrossed complexes of groups’, i.e. chain complexes of nonabelian groups (Gn,δn) with an additional structure in the form of binary operations G1 × G1 → Gk. We associate to a pointed topological space X a hypercrossed complex (X); and the functor induces an equivalence between the homotopy category of connected CW-complexes and a localization of the category of hypercrossed complexes. The relationship between (X) and Whitehead's crossed complex II(X) is established by a Canonical Surjection p: (X) → II(X) , which is a quasi-isomorphism if and only if X is a J-complex. Algebraic models consisting of truncated chain-complexes with binary operations are deduced for n-types, and as an application we deduce a group-theoretic interpretation of the cohomology groups Hn(G, A).

P Carrasco - One of the best experts on this subject based on the ideXlab platform.

  • group theoretic algebraic models for homotopy types
    Journal of Pure and Applied Algebra, 1991
    Co-Authors: P Carrasco, Antonio M Cegarra
    Abstract:

    Abstract In this paper a nonabelian version of the Dold-Kan-Puppe theorem is provided, showing how the Moore-complex functor defines a full equivalence between the category of simplicial groups and the category of what is called ‘hypercrossed complexes of groups’, i.e. chain complexes of nonabelian groups (Gn,δn) with an additional structure in the form of binary operations G1 × G1 → Gk. We associate to a pointed topological space X a hypercrossed complex (X); and the functor induces an equivalence between the homotopy category of connected CW-complexes and a localization of the category of hypercrossed complexes. The relationship between (X) and Whitehead's crossed complex II(X) is established by a Canonical Surjection p: (X) → II(X) , which is a quasi-isomorphism if and only if X is a J-complex. Algebraic models consisting of truncated chain-complexes with binary operations are deduced for n-types, and as an application we deduce a group-theoretic interpretation of the cohomology groups Hn(G, A).

Joseph Glover - One of the best experts on this subject based on the ideXlab platform.

  • symmetry groups of markov processes and the diagonal principle
    Journal of Theoretical Probability, 1991
    Co-Authors: Joseph Glover
    Abstract:

    LetXt be a transient Markov process onE with potentialU and excessive measures Exc. Let Sym be the group of finely continuous bijections onE which leave Exc invariant. From each subgroupJ of Sym, we construct the spaceF ofJ orbits inE and the Canonical Surjection Ψ:E→F. We show that Ψ(Z1) is a strong Markov process onF, whereZt is obtained fromXt by anh transform and time change. IfH is a subgroup of Sym withHe={ϕ∈H: ϕ(e)=e} trivial, thenH induces a group structure onE. There is a function 0supermartingale multiplicative functionals are given, and a general framework is proposed.