论文标题
Cuntz代数II连续场的拓扑不变
A topological invariant for continuous fields of Cuntz algebras II
论文作者
论文摘要
我们研究了我们先前工作中引入的Cuntz代数$ \ Mathcal {o} _ {n+1} $连续场的不变域，并找到一种方法来获得$ \ Mathbb {m} _n（Mathcal {o} _ \ infty）$ n $ n $ n of d $ n of的连续字段不变的构造。根据布朗的表示性定理，这给出了$ \ mathcal {o} _ {n+1} $连续字段的同构类别的培训，以给$ \ mathbb {m} _n（\ m athcal {o} {o} _ _ \ iffty）$。结果，我们获得了M. dadarlat的分类结果的新证明，其连续字段的连续字段{o} _ {n+1} $由向量捆绑包产生，该载体与$ \ Mathbb {m} _n（\ Mathcal {\ Mathcal {o} _ \ \ infty）相对应。
We investigate an invariant for continuous fields of the Cuntz algebra $\mathcal{O}_{n+1}$ introduced in our previous work, and find a way to obtain a continuous field of $\mathbb{M}_n(\mathcal{O}_\infty)$ from that of $\mathcal{O}_{n+1}$ using the construction of the invariant. By Brown's representability theorem, this gives a bijection from the set of the isomorphism classes of continuous fields of $\mathcal{O}_{n+1}$ to those of $\mathbb{M}_n(\mathcal{O}_\infty)$. As a consequence, we obtain a new proof for M. Dadarlat's classification result of continuous fields of $\mathcal{O}_{n+1}$ arising from vector bundles, which corresponds to those of $\mathbb{M}_n(\mathcal{O}_\infty)$ stably isomorphic to the trivial field.
