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Taurida Journal of Computer Science Theory and Mathematics, 2018, Issue 2, Pages 90–97
(Mi tvim48)
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On $n$-homogeneous $C^*$-algebras over a two-dimensional compact oriented connected manifold
M. V. Shchukin Belarusian national technical university,
ul. Hmelnizkogo 9, Minsk, 220013, Belarus
Abstract:
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.
Citation:
M. V. Shchukin, “On $n$-homogeneous $C^*$-algebras over a two-dimensional compact oriented connected manifold”, Taurida Journal of Computer Science Theory and Mathematics, 2018, no. 2, 90–97
Linking options:
https://www.mathnet.ru/eng/tvim48 https://www.mathnet.ru/eng/tvim/y2018/i2/p90
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Abstract page: | 83 | Full-text PDF : | 24 |
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