arXiv 2005.032682020-05math.QAmath.OA

量子扭束

The Quantum Twistor Bundle

Sophie Emma Zegers, Wojciech Szymański

备注：: The statement in Theorem 4.2. is wrong, the error in the proof lies in the analysis of the joint spectrum. An analysis of irreducible representations of the quantum symplectic sphere where made in the paper "Quantum quaternion spheres" by Bipul Saurabh, where we indeed see that x1 is nonzero

摘要：

本文研究了由Bonechi，Ciccoli和Tarlini的量子瞬子丛构造成$U(1)$ -商的量子扭量丛.这是一个例子，一个局部平凡的非交换丛满足条件的框架最近提出的Brzezienski和Szymaenski。特别地，我们给出了“连续函数”在其非交换全空间上的相应的$C^*$ -代数的详细描述。此外，我们还分析了Landi，Pagani和Reina提出的一种不同的量子瞬子丛的构造，找到了它的多项式代数的基，并发现了它的包络$C^*$ -代数的一个有趣的和意想不到的特征.

英文摘要：

We investigate the quantum twistor bundle constructed as a $U(1)$-quotient of the quantum instanton bundle of Bonechi, Ciccoli and Tarlini. It is an example of a locally trivial noncommutative bundle fulfilling conditions of the framework recently proposed by Brzeziński and Szymański. In particular, we give a detailed description of the corresponding $C^*$-algebra of 'continuous functions' on its noncommutative total space. Furthermore, we analyse a different construction of a quantum instanton bundle due to Landi, Pagani and Reina, find a basis of its polynomial algebra and discover an intriguing and unexpected feature of its enveloping $C^*$-algebra.

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摘要：

英文摘要：

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