Geodesic
$2$-homogeneous $C^{*}$-algebras with the space of primitive ideals homeomorphic to a two-dimensional oriented compact connected manifold generated by idempotents
Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2018), pp. 4-9 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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M. V. Shchukin. $2$-homogeneous $C^{*}$-algebras with the space of primitive ideals homeomorphic to a two-dimensional oriented compact connected manifold generated by idempotents. Journal of the Belarusian State University. Mathematics and Informatics, Tome 1 (2018), pp. 4-9. http://geodesic.mathdoc.fr/item/BGUMI_2018_1_a0/

[1] A. Bottcher, I. Gohberg, Y. Karlovich, “Banach algebras generated by N idempotents and applications”, Oper. Theory, 90 (1996), 19–54 | DOI | MR | Zbl

[2] A. Antonevich, N. Krupnik, “On trivial and non-trivial n-homogeneous C*-algebras”, Integr. Equ. Oper. Theory, 38(2) (2000), 172–189 | DOI | MR | Zbl

[3] M. V. Schukin, “Netrivialnaya S*-algebra, porozhdennaya chetyrmya idempotentami”, Institut matematiki NAN Belarusi, 9 (2001), 161–163

[4] M. Shchukin, “Non-trivial C*-algebras generated by idempotents”, Proceedings of the International Conference on Nonlinear Operators, Differential Equations and Applications : semin on fixed point theory Cluj-Napoca, 3 (2002), 353–359 | MR

[5] N. Krupnik, S. Roch, B. Silbermann, “On C*-algebras generated by idempotents”, Functional Analysis, 137(2) (1996), 303–319 | DOI | MR | Zbl

[6] V. І. Rabanovich, “Matrichni banakhovi algebri i teoriya zobrazhen”, Dissertatsiya. Kiev, 2000

[7] M. V. Schukin, “n-Odnorodnye S*-algebry s prostranstvom primitivnykh idealov, gomeomorfnym orientiruemomu kompaktnomu dvumernomu mnogoobraziyu”, Vestsi NAN Belarusi. Seryya fizika-matematychnykh navuk, 2 (2010), 12–17

[8] U. Massi, “Algebraicheskaya topologiya”, Mir, 1977 | MR