graded KK^G 理论的普适性质
K理论与同调
2026-04-07 v2 算子代数
摘要
对于 Z₂ 分段的 C* 代数，建立了 groupoid 等变 KK^G 理论的范畴论普适特征，通过观察“KK 公理”实现：对于每个 [s, E ⊕ B, F] ∈ KK^G(A,B)，“角嵌入” * 同态 j: B → cl(E_B(E ⊕ B) + s(A) + F · s(A)) 在 KK^G 中是可逆的。该 KK 公理和同伦不变性完全刻画了 graded KK^G 理论的普适性，从而直接扩展了 Higson 关于未分段 C* 代数 KK 理论通过稳定性、同伦不变性和 splitexactness characterization。
引用
@article{arxiv.2603.23157,
title = {The universal property of graded $KK^G$-theory},
author = {Bernhard Burgstaller},
journal= {arXiv preprint arXiv:2603.23157},
year = {2026}
}
备注
Attention, the paper is wrong! Unfortunately, I made a sign mistake at one position in the paper, namely, I overlooked that because the commutator is graded, [ F s(a), F] has an opposite sign in the difference than [ s(a), F], and so a used Kasparov element [ id_X, J, F] is unjustified. This is already obvious in Definition 4.1.(ii)