ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 22 Nov 2019 23:47:42 GMT2019-11-22T23:47:42Z5091- Protective multi-resolution analyses for L 2 (ℝ 2)https://scholarbank.nus.edu.sg/handle/10635/103984Title: Protective multi-resolution analyses for L 2 (ℝ 2)
Authors: Packer, J.A.; Rieffel, M.A.
Abstract: We define the notion of "projective" multiresolution analyses, for which, by definition, the initial space corresponds to a finitely generated projective module over the algebra C (∥ n) of continuous complex-valued functions on an n -torus. The case of ordinary multi-wavelets is that in which the projective module is actually free. We discuss the properties of pmjective multiresolution analyses, including the frames which they provide for L 2(ℝ n). Then we show how to construct examples for the case of any diagonal 2×2 dilation matrix with integer entries, with initial module specified to be any fixed finitely generated projective C(T 2)-module. We compute the isomorphism classes of the corresponding wavelet modules. © 2004 birkhäuser boston. All rights reserved.
Thu, 01 Jan 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1039842004-01-01T00:00:00Z
- The cohomology of the integer Heisenberg groupshttps://scholarbank.nus.edu.sg/handle/10635/104264Title: The cohomology of the integer Heisenberg groups
Authors: Lee, S.T.; Packer, J.A.
Abstract: We give a closed formula for the cohomology groups of the standard integer lattice in the simply-connected Heisenberg Lie group of dimension 2n + 1, n ∈ Z+. We also provide a recursion relation involving n for these cohomology groups. © 1996 Academic Press, Inc.
Thu, 15 Aug 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1042641996-08-15T00:00:00Z
- Wavelet filter functions, the matrix completion problem, and projective modules over C(double-struck T signn)https://scholarbank.nus.edu.sg/handle/10635/104705Title: Wavelet filter functions, the matrix completion problem, and projective modules over C(double-struck T signn)
Authors: Packer, J.A.; Rieffel, M.A.
Abstract: We discuss how one can use certain filters from signal processing to describe isomorphisms between certain projective C(double-struck T signn)-modules. Conversely, we show how cancellation properties for finitely generated projective modules over C(double-struck T signn) can often be used to prove the existence of continuous high pass filters, of the kind needed for multivariate wavelets, corresponding to a given continuous low-pass filter. However, we also give an example of a continuous low-pass filter for which it is impossible to find corresponding continuous high-pass filters. In this way we give another approach to the solution of the matrix completion problem for filters of the kind arising in wavelet theory.
Wed, 01 Jan 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1047052003-01-01T00:00:00Z
- The Primitive Ideal Space of Two-Step Nilpotent Group C*-Algebrashttps://scholarbank.nus.edu.sg/handle/10635/104336Title: The Primitive Ideal Space of Two-Step Nilpotent Group C*-Algebras
Authors: Baggett, L.; Packer, J.
Abstract: Let N be a two-step nilpotent, locally compact, second countable group having center Z and quotient A = N/Z. We study the Jacobson topology on the primitive ideal space Prim C*(N) of the group C*-algebra of N. We are able to describe this topology in terms of convergence of subgroup-representation pairs, as used by the first author in an earlier work. Under appropriate conditions on N, we are able to describe Prim C*(N) globally as the quotient of a principal Â bundle over Ẑ modulo an equivalence relation determined entirely by the group structure. We use this second result to compute the primitive ideal spaces of several examples, including all finitely generated, non-torsion two-step nilpotent discrete groups of rank less than or equal to five. Applications of our methods to more general central twisted crossed products are discussed. © 1994 Academic Press. All rights reserved.
Thu, 01 Sep 1994 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1043361994-09-01T00:00:00Z
- The equivariant brauer group and twisted transformation group c*-algebrashttps://scholarbank.nus.edu.sg/handle/10635/104286Title: The equivariant brauer group and twisted transformation group c*-algebras
Authors: Packer, J.A.
Abstract: Twisted transformation group C*-algebras associated to locally compact dynamical systems (X = Y/N, G) are studied, where G is abelian, N is a closed subgroup of G, and Y is a locally trivial principal G-bundle over Z = Y/G. An explicit homomorphism between H2(G, C(X, double-struck T sign)) and the equivariant Brauer group of Crocker, Kumjian, Raeburn and Williams, BrN(Z), is constructed, and this homomorphism is used to give conditions under which a twisted transformation group C*-algebra C0(X) ×τ,ω G will be strongly Morita equivalent to another twisted transformation group C*-algebra C0(Z) ×Id,ω N. These results are applied to the study of twisted group C*-algebras C* (Γ, μ) where Γ is a finitely generated torsion free two-step nilpotent group.
Wed, 01 Dec 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1042861999-12-01T00:00:00Z
- Crossed product C*-algebras and algebraic topologyhttps://scholarbank.nus.edu.sg/handle/10635/103087Title: Crossed product C*-algebras and algebraic topology
Authors: Packer, J.A.
Abstract: We discuss some recent developments that illustrate the interplay between the theory of crossed products of continuous trace C*-algebras and algebraic topology, summarizing results relating topological invariants coming from the theory of fiber bundles to continuous trace C*-algebras and their automorphism groups and the structure of the associated crossed product C*-algebras. This survey article starts from the classical theory of Dixmier, Douady, and Fell, and discusses the more recent work of Echterhoff, Phillips, Raeburn, Rosenberg, and Williams, among others. The topological invariants involved are Čech cohomology, the cohomology of locally compact groups with Borel cochains of C. Moore, and the recently introduced equivariant cohomology theory of Crocker, Kumjian, Raeburn and Williams.
Wed, 01 May 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1030871996-05-01T00:00:00Z
- Moore cohomology and central twisted crossed product C*-algebrashttps://scholarbank.nus.edu.sg/handle/10635/103572Title: Moore cohomology and central twisted crossed product C*-algebras
Authors: Packer, J.A.
Abstract: Let G be a locally compact second countable group, let X be a locally compact second countable Hausdorff space, and view C(X, T) as a trivial G-module. For G countable discrete abelian, we construct an isomorphism between the Moore cohomology group Hn(G, C(X, T)) and the direct sum Ext(Hn-1(G), Ȟ1 (βX, Z)) ⊕ C(X, Hn (G, T)); here Ȟ1 (βX, Z) denotes the first Čech cohomology group of the Stone-Čech compactification of X, βX, with integer coefficients. For more general locally compact second countable groups G, we discuss the relationship between the Moore group H2(G, C(X, T)), the set of exterior equivalence classes of element-wise inner actions of G on the stable continuous trace C*-algebra C0(X) ⊗ K-fraktur sign, and the equivariant Brauer group BrG(X) of Crocker, Kumjian, Raeburn, and Williams. For countable discrete abelian G acting trivially on X, we construct an isomorphism BrG(X) ≅ Ȟ3(X, Z) ⊕ H-fraktur signP-fraktur sign(X, G-fraktur sign̂) ⊕ C(X,H2(G, T)); here H-fraktur signP-fraktur sign(X, G-fraktur sign̂) is the group of equivalence classes of principal Ĝ bundles over X first considered by Raeburn and Williams.
Thu, 01 Feb 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1035721996-02-01T00:00:00Z
- K-theory for C*-algebras associated to lattices in Heisenberg Lie groupshttps://scholarbank.nus.edu.sg/handle/10635/103466Title: K-theory for C*-algebras associated to lattices in Heisenberg Lie groups
Authors: Lee, S.T.; Packer, J.A.
Abstract: We present methods for computing the K-groups of a variety of C*-algebras associated to lattices in Heisenberg Lie groups, including twisted group C*-algebras and Azumaya algebras over the corresponding nilmanifolds. A precise formula for the rank of the above K-groups is given, and it is shown that any twisted group C*-algebra over such a lattice Γ is KK-equivalent to an ordinary group C*-algebra corresponding to a possibly different lattice Γ0. We also give applications of our methods to the calculation of K-groups for certain twisted transformation group C*-algebras and certain continuous trace algebras whose spectra are tori.
Mon, 01 Jan 1996 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1034661996-01-01T00:00:00Z
- K-theory for the integer Heisenberg groupshttps://scholarbank.nus.edu.sg/handle/10635/103467Title: K-theory for the integer Heisenberg groups
Authors: Aslaksen, H.; Lee, S.T.; Packer, J.
Abstract: We give a closed formula for topological K-theory of the homogeneous space N/Γ, where Γ is the standard integer lattice in the simply connected Heisenberg Lie group N of dimension 2n + 1, n ∈ ℤ+. The main tools in our calculations are obtained by computing diagonal forms for certain incidence matrices that arise naturally in combinatorics. © 1999 Kluwer Academic Publishers.
Fri, 01 Jan 1999 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1034671999-01-01T00:00:00Z