Geodesic
On $n$-homogeneous $C^*$-algebras over a two-dimensional compact oriented connected manifold
Taurida Journal of Computer Science Theory and Mathematics, no. 2 (2018), pp. 90-97

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We consider the $n$-homogeneous $C^*$-algebras over a two-dimensional compact oriented connected manifold. Suppose $A$ be the $n$-homogeneous $C^*$-algebra with space of primitive ideals homeomorphic to a two-dimensional connected oriented compact manifold $P(A)$. It is well known that the manifold $P(A)$ is homeomorphic to the sphere $P_k$ glued together with $k$ handles in the hull-kernel topology. On the other hand, the algebra $A$ is isomorphic to the algebra $\Gamma (E)$ of continuous sections for the appropriate algebraic bundle $E$. The base space for the algebraic bundle is homeomorphic to the set $P_k$. By using this geometric realization, we described the class of non-isomorphic $n$-homogeneous ($n\geq 2$) $C^*$-algebras over the set $P_k$. Also, we calculated the number of non-isomorphic $n$-homogeneous $C^*$-algebras over the set $P_k$.
Keywords: $C^*$-algebra, primitive ideals, base space, algebraic bundle, operator algebra, irreducible representation. 
@article{TVIM_2018_2_a5,
     author = {M. V. Shchukin},
     title = {On $n$-homogeneous $C^*$-algebras over a two-dimensional compact oriented connected manifold},
     journal = {Taurida Journal of Computer Science Theory and Mathematics},
     pages = {90--97},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVIM_2018_2_a5/}
}
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M. V. Shchukin. On $n$-homogeneous $C^*$-algebras over a two-dimensional compact oriented connected manifold. Taurida Journal of Computer Science Theory and Mathematics, no. 2 (2018), pp. 90-97. http://geodesic.mathdoc.fr/item/TVIM_2018_2_a5/