|
Таврический вестник информатики и математики, 2018, выпуск 2, страницы 90–97
(Mi tvim48)
|
|
|
|
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
Аннотация:
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 $P_k$.
Ключевые слова:
$C^*$-algebra, primitive ideals, base space, algebraic bundle, operator algebra, irreducible representation.
Образец цитирования:
M. V. Shchukin, “On $n$-homogeneous $C^*$-algebras over a two-dimensional compact oriented connected manifold”, ТВИМ, 2018, no. 2, 90–97
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/tvim48 https://www.mathnet.ru/rus/tvim/y2018/i2/p90
|
Статистика просмотров: |
Страница аннотации: | 83 | PDF полного текста: | 24 |
|