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Axioms 2018, 7(4), 79;

Extending Characters of Fixed Point Algebras

Department of Mathematics and Natural Sciences, Blekinge Tekniska Högskola, 371 41 Karlskrona, Sweden
Received: 13 October 2018 / Revised: 2 November 2018 / Accepted: 5 November 2018 / Published: 7 November 2018
(This article belongs to the Collection Topological Groups)
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A dynamical system is a triple ( A , G , α ) consisting of a unital locally convex algebra A, a topological group G, and a group homomorphism α : G Aut ( A ) that induces a continuous action of G on A. Furthermore, a unital locally convex algebra A is called a continuous inverse algebra, or CIA for short, if its group of units A × is open in A and the inversion map ι : A × A × , a a 1 is continuous at 1 A . Given a dynamical system ( A , G , α ) with a complete commutative CIA A and a compact group G, we show that each character of the corresponding fixed point algebra can be extended to a character of A. View Full-Text
Keywords: dynamical system; continuous inverse algebra; character; maximal ideal; fixed point algebra; extension dynamical system; continuous inverse algebra; character; maximal ideal; fixed point algebra; extension
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Wagner, S. Extending Characters of Fixed Point Algebras. Axioms 2018, 7, 79.

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