37,730 research outputs found
Logic Programming with Graph Automorphism: Integrating naut with Prolog (Tool Description)
This paper presents the plnauty~library, a Prolog interface to the nauty
graph-automorphism tool. Adding the capabilities of nauty to Prolog combines
the strength of the "generate and prune" approach that is commonly used in
logic programming and constraint solving, with the ability to reduce symmetries
while reasoning over graph objects. Moreover, it enables the integration of
nauty in existing tool-chains, such as SAT-solvers or finite domain constraints
compilers which exist for Prolog. The implementation consists of two
components: plnauty, an interface connecting \nauty's C library with Prolog,
and plgtools, a Prolog framework integrating the software component of nauty,
called gtools, with Prolog. The complete tool is available as a SWI-Prolog
module. We provide a series of usage examples including two that apply to
generate Ramsey graphs. This paper is under consideration for publication in
TPLP.Comment: Paper presented at the 32nd International Conference on Logic
Programming (ICLP 2016), New York City, USA, 16-21 October 201
A multiplier approach to the Lance-Blecher theorem
A new approach to the Lance-Blecher theorem is presented resting on the
interpretation of elements of Hilbert C*-module theory in terms of multiplier
theory of operator C*-algebras: The Hilbert norm on a Hilbert C*-module allows
to recover the values of the inducing C*-valued inner product in a unique way,
and two Hilbert C*-modules {M_1, _1}, {M_2, _2} are isometrically
isomorphic as Banach C*-modules if and only if there exists a bijective
C*-linear map S: M_1 --> M_2 such that the identity _1 \equiv
_2 is valid. In particular, the values of a C*-valued inner product
on a Hilbert C*-module are completely determined by the Hilbert norm induced
from it. In addition, we obtain that two C*-valued inner products on a Banach
C*-module inducing equivalent norms to the given one give rise to isometrically
isomorphic Hilbert C*-modules if and only if the derived C*-algebras of
''compact'' module operators are *-isomorphic. The involution and the C*-norm
of the C*-algebra of ''compact'' module operators on a Hilbert C*-module allow
to recover its original C*-valued inner product up to the following equivalence
relation: _1 \sim _2 if and only if there exists an invertible,
positive element of the center of the multiplier C*-algebra M(A) of A such
that the identity _1 \equiv a \cdot _2 holds.Comment: Plain TeX, 9 pages, without figures, submitted to Zeitschrift Anal.
Anwendunge
Injective envelopes and local multiplier algebras of C*-algebras
The local multiplier C*-algebra M_{loc}(A) of any C*-algebra A can
*-isomorphicly embedded into the injective envelope I(A) of A in such a way
that the canonical embeddings of A into both these C*-algebras are identified.
If A is commutative then M_{loc}(A) = I(A) . The injective envelopes of A and
M_{loc}(A) always coincide, and every higher order local multiplier C*-algebra
of A is contained in the regular monotone completion \bar{A} in I(A) of A . In
case the set Z(A).A is dense in A the center of the local multiplier C*-algebra
of A is the local multiplier C*-algebra of the center of A, and both they are
*-isomorphic to the injective envelope of the center of A . A Wittstock type
extension theorem for completely bounded bimodule maps on operator bimodules
taking values in M_{loc}(A) is proven to hold if and only if M_{loc}(A) = I(A).
In general, a solution of the problem for which C*-algebras A the C*-algebras
M_{loc}(A) is injective is shown to be equivalent to the solution of I.
Kaplansky's 1951 problem whether all AW*-algebras are monotone complete.Comment: 10 pages, LaTeX2e, one statement and its proof correcte
Isomorphisms of Hilbert C*-Modules and -Isomorphisms of Related Operator C*-Algebras
Let be a Banach C*-module over a C*-algebra carrying two
-valued inner products , which induce equivalent to
the given one norms on . Then the appropriate unital C*-algebras of
adjointable bounded -linear operators on the Hilbert -modules and are shown to be
-isomorphic if and only if there exists a bounded -linear isomorphism
of these two Hilbert -modules satisfying the identity . This result extends other equivalent descriptions due to
L.~G.~Brown, H.~Lin and E.~C.~Lance. An example of two non-isomorphic Hilbert
C*-modules with -isomorphic C*-algebras of ''compact''/adjointable bounded
module operators is indicated.Comment: 5 pages, LaTeX fil
Spectral and polar decomposition in AW*-algebras
We show the possibility and the uniqueness of polar decomposition of elements
of arbitrary AW*-algebras inside them. We prove that spectral decomposition of
normal elements of normal AW*-algebras is possible and unique inside them. The
possibility of spectral decomposition of normal elements does not depend on the
normality of the AW*-algebra under consideration.Comment: 7 pages, LATEX, preprint NTZ-25/91 (Universitaet Leipzig,
Naturwissenschaftlich-Theoretisches Zentrum, 1991), submitted to Zeitschr.
Anal. An
The Standard Model - the Commutative Case: Spinors, Dirac Operator and de Rham Algebra
The present paper is a short survey on the mathematical basics of Classical
Field Theory including the Serre-Swan' theorem, Clifford algebra bundles and
spinor bundles over smooth Riemannian manifolds, Spin^C-structures, Dirac
operators, exterior algebra bundles and Connes' differential algebras in the
commutative case, among other elements. We avoid the introduction of principal
bundles and put the emphasis on a module-based approach using Serre-Swan's
theorem, Hermitian structures and module frames. A new proof (due to Harald
Upmeier) of the differential algebra isomorphism between the set of smooth
sections of the exterior algebra bundle and Connes' differential algebra is
presented.Comment: 19 pages, LaTeX2
Characterizing C*-algebras of compact operators by generic categorical properties of Hilbert C*-modules
B. Magajna and J. Schweizer showed in 1997 and 1999, respectively, that
C*-algebras of compact operators can be characterized by the property that
every norm-closed (and coinciding with its biorthogonal complement, resp.)
submodule of every Hilbert C*-module over them is automatically an orthogonal
summand. We find out further generic properties of the category of Hilbert
C*-modules over C*-algebras which characterize precisely the C*-algebras of
compact operators.Comment: 9 pages, part of a collection dedicated to the memory of Yu. P.
Solovyov (Moscow State University). to appear in K-Theor
Direct integrals and Hilbert W*-Modules
Investigating the direct integral decomposition of von Neumann algebras of
bounded module operators on self-dual Hilbert W*-moduli an equivalence
principle is obtained which connects the theory of direct disintegration of von
Neumann algebras on separable Hilbert spaces and the theory of von Neumann
representations on self-dual Hilbert {\bf A}-moduli with countably generated
{\bf A}-pre-dual Hilbert {\bf A}-module over commutative separable W*-algebras
{\bf A}. Examples show posibilities and bounds to find more general relations
between these two theories, (cf. R. Schaflitzel's results). As an application
we prove a Weyl--Berg--Murphy type theorem: For each given commutative
W*-algebra {\bf A} with a special approximation property (*) every normal
bounded {\bf A}-linear operator on a self-dual Hilbert {\bf A}-module with
countably generated {\bf A}-pre-dual Hilbert {\bf A}-module is decomposable
into the sum of a diagonalizable normal and of a ''compact'' bounded {\bf
A}-linear operator on that module.Comment: 20 pages, LATEX file, preprint 23/91, NTZ, Univ. Leipzig, German
Hilbertian versus Hilbert W*-modules, and applications to - and other invariants
Hilbert(ian) A-modules over finite von Neumann algebras A with a faithful
normal trace state (from global analysis) and Hilbert W*-modules over A (from
operator algebra theory) are compared, and a categorical equivalence is
established. The correspondence between these two structures sheds new light on
basic results in -invariant theory providing alternative proofs. We
indicate new invariants for finitely generated projective B-modules, where B is
supposed any unital C*-algebra, (usually the full group C*-algebra
of the fundamental group of a manifold ). The results are of
interest to specialists in operator algebras and global analysis.Comment: 12 pages, Latex2
Hilbert H*-modules and Hilbert modules over (non-self-adjoint) operator algebras -- a reference overview II
The two reference lists contain 54/22 references of papers and preprints
concerned with the theory and/or various applications of Hilbert modules over
Hilbert -algebras and over (non-self-adjoint) operator algebras. They are
far from being complete, but they give additional information about two
research fields which are closely related to the theory of Hilbert C*-modules,
i.e. they are complements to the reference guide about this circle of problems.
Any additions, corrections and forthcoming information are welcome.Comment: LaTeX 2.09, 5 page
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