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On continuous fields of JB-algebras

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arxiv 0803.3598 v1 pith:NGHHYXIQ submitted 2008-03-25 math.OA math.FA

classification math.OAmath.FA
keywords continuousjb-algebrasalgebrasa-sub-talgebrabelongsdecompositionenveloping
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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.

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