AI 中文总结
本文采用李-泊松代数的矩阵正则化方法，通过将代数簇分解为余伴随轨道构造其量子化，并以模糊$S^7$的详细构造作为实例。
AI 中文摘要
我们研究对由紧致半单李代数的卡西米尔多项式相关方程定义的代数簇进行量子化，这类卡西米尔多项式属于对应李-泊松代数的泊松中心。为此，我们采用近期提出的李-泊松代数矩阵正则化方法，尤其利用其基于可约表示的形式，通过将代数簇分解为包含奇异轨道的余伴随轨道，来构造这些代数簇的量子化。作为具体实例，我们详细给出了模糊$S^7$的构造过程。
英文摘要
We study the quantization of algebraic varieties defined by equations involving Casimir polynomials of compact semisimple Lie algebras. The Casimir polynomials belong to the Poisson center of the corresponding Lie-Poisson algebra. For this purpose, we employ a recently developed matrix regularization of Lie-Poisson algebras. In particular, using its formulation based on reducible representations, we construct quantizations of these algebraic varieties through their decomposition into coadjoint orbits, including singular orbits. As a concrete example, we present the construction of fuzzy $S^7$ in detail.
Comments37 pages, no figures
