Renault, Wassermann, Handelman and Rossmann (early 1980s) and Evans and Gould (1994) explicitly described the [Formula: see text]-theory of certain unital AF-algebras [Formula: see text] as (quotients of) polynomial rings. In this paper, we show that in each case the multiplication in the polynomial ring (quotient) is induced by a ∗-homomorphism [Formula: see text] arising from a unitary braiding on a C*-tensor category and essentially defined by Erlijman and Wenzl (2007). We also present some new explicit calculations based on the work of Gepner, Fuchs and others. Specifically, we perform computations for the rank two compact Lie groups SU(3), Sp(4) and G2 that are analogous to the Evans–Gould computation for the rank one compact Lie group SU(2).The Verlinde rings are the fusion rings of Wess–Zumino–Witten models in conformal field theory or, equivalently, of certain related C*-tensor categories. Freed, Hopkins and Teleman (early 2000s) realized these rings via twisted equivariant [Formula: see text]-theory. Inspired by this, our long-term goal is to realize these rings in a simpler [Formula: see text]-theoretical manner, avoiding the technicalities of loop group analysis. As a step in this direction, we note that the Verlinde rings can be recovered as above in certain special cases.

中文翻译：

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来自编织 C*-张量类别的 AF-代数的 K-理论

Renault、Wassermann、Handelman 和 Rossmann（1980 年代初期）以及 Evans 和 Gould（1994 年）明确地将 [公式：参见文本]-某些单位 AF 代数 [公式：参见文本] 的理论描述为多项式环的（商）。在本文中，我们表明，在每种情况下，多项式环（商）中的乘法都是由 *-同态 [公式：见正文] 引起的，该同态是由 C*-张量类别上的酉编织产生的，并且基本上由 Erlijman 和文茨（2007）。我们还根据 Gepner、Fuchs 和其他人的工作提出了一些新的显式计算。具体来说，我们对秩为二的紧李群 SU(3)、Sp(4) 和 G 进行计算2这类似于对一阶紧李群 SU(2) 的 Evans-Gould 计算。 Verlinde 环是共形场论中 Wess-Zumino-Witten 模型的融合环，或者等效地，某些相关 C*-张量的融合环类别。Freed、Hopkins 和 Teleman（2000 年代初期）通过扭曲等变 [公式：见正文] 理论实现了这些环。受此启发，我们的长期目标是以更简单的 [公式：见正文] 理论方式实现这些环，避免环群分析的技术性问题。作为朝着这个方向迈出的一步，我们注意到在某些特殊情况下可以如上恢复 Verlinde 环。