An Explicit Duality for Finite Groups

Details An Explicit Duality for Finite Groups An Explicit Duality for Finite Groups

2005-11-07

arxiv.org/abs/math/0511126v1

Mathematics

Operator Algebras

Scientific paper

Using a ``3 by 3 matrix trick'' we previously showed that multiplication in a C*-algebra A, an algebraic structure, is determined by the geometry of the C*-algebra of the 3 by 3 matrices with entries from A. As an application of this algebra-geometry duality we now construct an order theoretic based duality theory for all groups which are either locally compact abelian or finite. This construction generalizes the van Kampen--Pontriagin duality for locally compact abelian groups.

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