论文标题
$ c^\ ast $ - 类别的e理论
E-theory for $C^\ast$-Categories
论文作者
论文摘要
$ e $ - 理论最初是由Connes和Higson确定的，并在此施工之后进行了进一步的工作。我们将定义概括为$ c^\ ast $ - 类别。 $ c^\ ast $ - 类别被制定为在分类图片中赋予操作者代数理论，并在数学物理学的研究中起重要作用。在这种情况下，它们类似于$ c^\ ast $ -Algebras，因此定义的不变性来自$ c^\ ast $ -Algebra理论，但它们尚未定义$ e $ - 理论。在这里，我们定义了$ e $ - 用于复杂和真实分级的$ c^\ ast $ - 类别的理论，并证明其具有与$ e $ - 理论相似的$ c^\ ast $ algebras。
$E$-theory was originally defined concretely by Connes and Higson and further work followed this construction. We generalise the definition to $C^\ast$-categories. $C^\ast$-categories were formulated to give a theory of operator algebras in a categorical picture and play important role in the study of mathematical physics. In this context, they are analogous to $C^\ast$-algebras and so have invariants defined coming from $C^\ast$-algebra theory but they do not yet have a definition of $E$-theory. Here we define $E$-theory for both complex and real graded $C^\ast$-categories and prove it has similar properties to $E$-theory for $C^\ast$-algebras.
