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Journal of Operator Theory

Volume 88, Issue 1, Summer 2022  pp. 3-36.

On continuous duality for Moore groups

Authors:  Sergei S. Akbarov
Author institution: School of Applied Mathematics, National Research University Higher School of Economics, 34, Tallinskaya St. Moscow, 123458 Russia

Summary: In 2013, Yu.N.~Kuznetsova constructed a duality theory for Moore groups, based on the idea of a continuous envelope of topological algebra and having the advantage over the existing theories that its enveloping category consists of Hopf algebras in the classical sense. Unfortunately, her work contains several errors, due to which her theory can be considered proved only for a narrower class of groups of the form ${\mathbb R}^n\times K\times D$, where $K$ is a compact group and $D$ a discrete Moore group. In this paper we correct the errors of Kuznetsova's work and prove the validity (up to some specifications in terminology) of her theory for all Moore groups.

Keywords: stereotype space, stereotype algebra, envelope, duality

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