Ernst Binz

A subgroup theorem for free products of pro-finite groups

Fakzrltcit fiir Mathematik und Injoormatik, Universitiit, 68, Mannheim, West Gwmaq~ Communicated by P. A%f. Cohn Received July 13, 1970 The notion of a free product of pro-finite groups has some important applications in the theory of algebraic number fields (see [3]). In this connection, it is interesting to get some knowledge about the subgroups of such a free product. The aim of this paper is to show a theorem for the open subgroups of a free pro-finite product, which is an analog of Kurosh’s well- known subgroup theorem for the free products of discrete groups in the usual sense. By K we denote a class of finite groups, which is closed under formation of subgroups, factorgroups and group extensions (c.g., all finite groups, the solvable groups, the p-groups, etc.) By a puo-@roup 6 we understand a projective limit 6 7 I;m Gi of groups Gi E (5. Let 6, , E E 81, be a family of pro-K-groups. A family of homomorphisms 7% : Cc,, + -5 into a pro-K-group

Construction and uniqueness of the C*-Weyl algebra over a general pre-symplectic space

j is called convergent, if every open subgroup of

Nonholonomic constraints in classical field theories

contains almost every (i.e., up to a finite number) of the images ~~(05~). This condition is clearly empty, if VI is a finite index set. The free pro-K- pvoducc of the pro-K-groups 6, is now defined as to be a pro-K-group (5 =: JJ&,[ . 6, , together with a convergent family of homomorphisms with the following universal property: If y,? : (ci,> ---f & is any convergent 104

The Geometry of Heisenberg Groups: With Applications in Signal Theory, Optics, Quantization, and Field Quantization

A systematic approach to the C*-Weyl algebra W(E,σ) over a possibly degenerate pre-symplectic form σ on a real vector space E of possibly infinite dimension is elaborated in an almost self-contained manner. The construction is based on the theory of Kolmogorov decompositions for σ-positive-definite functions on involutive semigroups and their associated projective unitary group representations. The σ-positive-definite functions provide also the C*-norm of W(E,σ), the latter being shown to be *-isomorphic to the twisted group C*-algebra of the discrete vector group E. The connections to related constructions are indicated. The treatment of the fundamental symmetries is outlined for arbitrary pre-symplectic σ. The construction method is especially applied to the trivial symplectic form σ=0, leading to the commutative Weyl algebra over E, which is shown to be isomorphic to the C*-algebra of the almost periodic continuous function on the topological dual Eτ′ of E with respect to an arbitrary locally convex Ha...

On a Marinescu structure on C(X)

Abstract A multisymplectic setting for classical field theories subject to nonholonomic constraints is presented. The infinite-dimensional setting in the space of Cauchy data is also given.

Heisenberg groups: a unifying structure of signal theory, holography and quantum information theory

The skew field of quaternions Elements of the geometry of

Vector Fields in Three-Space, Natural Internal Degrees of Freedom, Signal Transmission and Quantization

S^3

On a smooth geometric approach to the dynamics of media with microstructures

, Hopf bundles and spin representations Internal variables of singularity free vector fields in a Euclidean space Isomorphism classes, Chern classes and homotopy classes of singularity free vector fields in three-space Heisenberg algebras, Heisenberg groups, Minkowski metrics, Jordan algebras and SL

Symmetry, Constitutive Laws of Bounded Smoothly Deformable Media and Neumann Problems

(2,\mathbb {C})

On the irredundant part of the first Piola-Kirchhoff stress tensor

The Heisenberg group and natural