二重米尔诺幂对于多重回溯量子复射影平面
Rank-two Milnor idempotents for the multipullback quantum complex projective plane
AI总结：
本文研究了多重回溯量子复射影平面的C*-代数的K₀群，证明了米尔诺模与非交换向量丛或其补集的同构关系，并展示了其中一个米尔诺模可分解为自由模与非自由投射模的直和。
摘要：
多重回溯量子复射影平面的C*-代数的K₀群已知为Z³，其中一个是C*-代数本身，一个是非交换（对偶）tautological线丛的截面模，另一个是与Calow-Matthes量子3球面C*-代数的K₁群生成元相关的米尔诺模。本文证明这些米尔诺模要么与SU_q(2)-延长的Heegaard量子5球面S⁵_H作为U(1)-量子主丛关联的非交换向量丛的截面模同构，要么是秩四自由模的补集。最后，证明其中一个米尔诺模总是分解为秩一自由模和一个不与S⁵_H关联的秩一非自由投射模的直和。
英文摘要：
The $K_0$-group of the C*-algebra of multipullback quantum complex projective plane is known to be $\mathbb{Z}^3$, with one generator given by the C*-algebra itself, one given by the section module of the noncommutative (dual) tautological line bundle, and one given by the Milnor module associated to a generator of the $K_1$-group of the C*-algebra of Calow-Matthes quantum 3-sphere. Herein we prove that these Milnor modules are isomorphic either to the section module of a noncommutative vector bundle associated to the $SU_q(2)$-prolongation of the Heegaard quantum 5-sphere $S^5_H$ viewed as a $U(1)$-quantum principal bundle, or to a complement of this module in the rank-four free module. Finally, we demonstrate that one of the above Milnor modules always splits into the direct sum of the rank-one free module and a rank-one non-free projective module that is \emph{not} associated with $S^5_H$.
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