Quantization of Algebraic Varieties Defined by Casimir Polynomials via Matrix Regularization: Fuzzy S⁷ and Beyond

2026/08/05 by Akifumi Sako
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP #msc:53D17 #msc:81S10 #msc:81T75 #msc:81T32

paper · pdf

37 pages, no figures

arxiv created 2026/08/05 · arxiv updated 2026/08/06

Abstract

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 S⁷ in detail.

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