Genuine‐commutative structure on rational equivariant K$K$‐theory for finite abelian groups
Genuine‐commutative structure on rational equivariant K$K$‐theory for finite abelian groups
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有理等变 K$K$ 的真正交换结构 - 有限阿贝尔群理论
DOI：
10.1112/blms.12616
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发表时间：
2022
影响因子：
0.9
通讯作者：
May, Clover
中科院分区：
文献类型：
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作者：
Bohmann, Anna Marie;Hazel, Christy;Ishak, Jocelyne;Kędziorek, Magdalena;May, Clover
在前人工作的基础上，证明了周期有理G$G$等变拓扑K$K$理论对有限交换群G$G$具有唯一的真可换环结构.这意味着每一个同伦群为KUQ，G$KU{\mathbb{q}，G}$的真交换环谱与KUQ，G$KU{\mathbb{q}，G}$弱等价。相反，联结有理等变K$K$-理论谱不具有真对易环结构的这种唯一性。
In this paper, the authors build on their previous work to show that periodic rational G$G$‐equivariant topological K$K$‐theory has a unique genuine‐commutative ring structure for G$G$ a finite abelian group. This means that every genuine‐commutative ring spectrum whose homotopy groups are those of KUQ,G$KU_{\mathbb {Q},G}$ is weakly equivalent, as a genuine‐commutative ring spectrum, to KUQ,G$KU_{\mathbb {Q},G}$. In contrast, the connective rational equivariant K$K$‐theory spectrum does not have this type of uniqueness of genuine‐commutative ring structure.