On continuous fields of JB-algebras

TL;DR

This paper introduces continuous fields of JB-algebras, explores their universal enveloping C*-algebras, and demonstrates a decomposition into continuous fields of C*-algebras, extending the structure theory of JB-algebras.

Contribution

It establishes a decomposition of the universal enveloping C*-algebra of a continuous field of JB-algebras into a continuous field of C*-algebras, advancing the understanding of JB-algebra structures.

Findings

Decomposition of universal enveloping C*-algebra into a continuous field of C*-algebras.

Extension of structure theory from JB-algebras to continuous fields.

Framework for analyzing continuous fields of JB-algebras.

Abstract

We introduce and study continuous fields of JB-algebras (which are real non-associate analogues of C*-algebras). In particular, we show that for the universal enveloping C*-algebra C*sub-u(B) for the JB-algebra B defined by a continuous field of JB-algebras A-sub-t, t belongs to T, on a locally compact space T, there exists a decomposition of C*-sub-u(B) into a continuous field of C*-algebras C*u(A-sub-t), t belongs to T, on the same space T, composed entirely of the universal enveloping C*-algebras of the corresponding JB-algebras from the aforementioned decomposition of the algebra B.