Real, Complex and Functional analysis

$2$-homogeneous $C^{*}$-algebras with the space of primitive ideals homeomorphic to a two-dimensional oriented compact connected manifold generated by idempotents

M. V. Shchukin

Belarusian National Technical University, 65 Niezaliežnasci Avenue, Minsk 220013, Belarus

Abstract: Before showed in 1961 that every n-homogeneous $C^{*}$-algebra is isomorphic to the algebra of all continuous sections for the appropriate algebraic bundle. The base space for the bundle is homeomorphic to the space of primitive ideals for the algebra in the appropriate topology. By using that we considered the $2$-homogeneous $C^{*}$-algebra $A$ such that the space of primitive ideals of the algebra is homeomorphic to a two-dimensional compact oriented connected manifold. We constructed three idempotents from the algebra $A$ that generated the algebra.

Keywords: $C^{*}$-algebra; idempotent; finite-dimensional irreducible representations; operator algebras; number of generators.

UDC: 517.986

Received: 10.07.2017