$C^\ast$ -范畴的E-理论
E-theory for $C^\ast$-Categories
摘要：
$E$ -理论最初是由Connes和Higson具体定义的，进一步的工作遵循这一结构。我们将定义推广到$C^\ast$ -范畴。$C^\ast$ -范畴是范畴图像中算子代数的理论，在数学物理的研究中起着重要的作用。在这种情况下，它们类似于$C^\ast$ -代数，因此具有来自$C^\ast$ -代数理论的定义的不变量，但它们还没有$E$ -理论的定义。本文定义了复和实分次$C^\ast$ -范畴的$E$ -理论，并证明了它与$C^\ast$ -代数的$E$ -理论具有相似的性质.
英文摘要：
$E$-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.
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