Geodesic
On $3$-homogeneous $C^{*}$-algebras over two-dimensional oriented manifolds
Taurida Journal of Computer Science Theory and Mathematics, no. 1 (2020), pp. 11-18 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider algebraic bundles over a two-dimensional compact oriented connected manifold. In 1961 J. Fell, J. Tomiyama, M. Takesaki showed that every $n$-homogeneous $C^{*}$-algebra is isomorphic to the algebra of all continuous sections for the appropriate algebraic bundle. By using this realization we prove in the work that every $3$-homogeneous $C^{*}$-algebra over two-dimensional compact oriented connected manifold can be generated by three idempotents. Such algebra can not be generated by two idempotents.
Keywords: $n$-homogeneous $C^{*}$-algebras idempotent two-dimensional manifold number of generators operator algebras. 
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     author = {M. V. Shchukin},
     title = {On $3$-homogeneous $C^{*}$-algebras over two-dimensional oriented manifolds},
     journal = {Taurida Journal of Computer Science Theory and Mathematics},
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     year = {2020},
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     url = {http://geodesic.mathdoc.fr/item/TVIM_2020_1_a0/}
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M. V. Shchukin. On $3$-homogeneous $C^{*}$-algebras over two-dimensional oriented manifolds. Taurida Journal of Computer Science Theory and Mathematics, no. 1 (2020), pp. 11-18. http://geodesic.mathdoc.fr/item/TVIM_2020_1_a0/