环上的量子群作用与等变K-理论
Quantum group actions on rings and equivariant K-theory
摘要：
设$\Uq$是一个量子群.对于一个具有$\Uq$ -对称性的（非交换）空间作为一个$\Uq$ -模代数$A$，我们可以认为$A$上的等变向量丛是具有相容$\Uq$ -作用的投射$A$ -模。利用Quillen的精确范畴，我们构造了这类量子向量丛的等变K-理论，并给出了计算方法.计算了经典型量子齐性空间和量子对称代数的等变K-群。
英文摘要：
Let $\Uq$ be a quantum group. Regarding a (noncommutative) space with $\Uq$-symmetry as a $\Uq$-module algebra $A$, we may think of equivariant vector bundles on $A$ as projective $A$-modules with compatible $\Uq$-action. We construct an equivariant K-theory of such quantum vector bundles using Quillen's exact categories, and provide means for its compution. The equivariant K-groups of quantum homogeneous spaces and quantum symmetric algebras of classical type are computed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
