arXiv subjects

Wend Werner

Publications and source records attributed to Wend Werner.

9 recordsLinked to original sources

arXiv2022

Extensions of special 3-fields

We investigate finite field extensions of the unital 3-field, consisting of the unit element alone, and find considerable differences to classical field theory. Furthermore, the structure of their automorphism groups is clarified and the respective subfields are determined. In an attempt to better understand the structure of 3-fields that show up here we look at ways in which new unital 3-fields can be obtained from known ones in terms of product structures, one of them the Cartesian product which has no analogue for binary fields.

math.RA↗

arXiv2020

Structure of unital 3-fields

We investigate fields in which addition requires three summands. These ternary fields are shown to be isomorphic to the set of invertible elements in a local ring $\mathcal{R}$ having $\mathbb{Z}\diagup 2\mathbb{Z}$ as a residual field. One of the important technical ingredients is to intrinsically characterize the maximal ideal of $\mathcal{R}$. We include a number of illustrative examples and prove that the structure of a finite 3-field is not connected to any binary field.

math.RA↗

arXiv2016

Inductive limits of finite dimensional hermitian symmetric spaces and K-theory

K-Theory for hermitian symmetric spaces of non-compact type, as developed recently by the authors, allows to put Cartan's classification into a homological perspective. We apply this method to the case of inductive limits of finite dimensional hermitian symmetric spaces. This might be seen as an indication of how much more powerful the homological theory is in comparison to the more classical approach. When seen from high above, we follow the path laid out by a similar result in the theory of C*-algebras. Important is a clear picture of the behavior of morphisms between bounded symmetric domains of finite dimensions, which is more complex than in the C*-case, as well as an accessible K-theory. We furthermore have to slightly modify the invariant from our previous work. Roughly, we use traces left by co-root lattices on K-groups, instead of co-roots themselves, which had been used previously.

math.KT↗

arXiv2012

K-theory of hermitian symmetric spaces and root lattices

This is a companion to a recent investigation of K-theoretical invariants for symmetric spaces. We introduce a new class of cycles in K-groups, which are connected to elements of an underlying root lattice. This will be needed for a K-theoretical classification of inductive limits.

math.KT↗

arXiv2012

The universal enveloping TRO of a JB*-triple system

We associate to every JB*-triple system a so-called universal enveloping TRO and show some functorial properties of this correspondence. We compute the universal enveloping TROs of the finite dimensional Cartan factors.

math.OA↗

arXiv2011

A K-theoretic approach to the classification of symmetric spaces

We show that the classification of the symmetric spaces can be achieved by K-theoretical methods. We focus on Hermitian symmetric spaces of non-compact type, and define K-theory for JB*-triples along the lines of C*-theory. K-groups have to be provided with further invariants in order to classify. Among these are the cycles obtained from so called grids, intimately connected to the root systems of an underlying Lie-algebra and thus reminiscent of the classical classification scheme.

math.OA↗

arXiv2010

Unbounded multipliers on operator spaces

We introduce unbounded multipliers on operator spaces. These multipliers generalize both, regular operators on Hilbert C*-modules and (bounded) multipliers on operator spaces.

math.OA↗

arXiv2007

Ordered involutive operator spaces

This is a companion to recent papers of the authors; here we construct the `noncommutative Shilov boundary' of a (possibly nonunital) selfadjoint ordered space of Hilbert space operators. The morphisms in the universal property of the boundary preserve order. As an application, we consider `maximal' and `minimal' unitizations of such ordered operator spaces.

math.OA↗

arXiv2003

Ordered C*-modules

In this first part of a study of ordered operator spaces, we develop the basic theory of `ordered C*-bimodules'. A crucial role is played by `open central tripotents', a JB*-triple variant of Akemann's notion of open projection.

math.OA↗