\textrmU(n)-structures and their induced minimal left ideals

2025/11/10 by Suárez, Ricardo
Mathematics · #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.48550/arxiv.2511.06900

openalex publication_date 2025/11/10 · openalex created_date 2025/11/12 · openalex updated_date 2026/07/28

Abstract

In previous work, we associated to \textrmSU(3), G₂, and \textrmSpin(7)-structures minimal left ideals for the Clifford algebras ℝ_0,6,ℝ_0,7, and ℝ_0,8, respectively. In this paper, we continue to analyze the link between Berger's classification theorem and the structure theorem of minimal left ideals for Clifford algebras of signature (p,q) by identifying U(n)-structures with minimal left ideals for Clifford algebras of various signatures via the induced Kahler polynomial P(ω₀) associated with the symplectic form ω₀ that defines the U(n)-structure as a stabilizer subgroup of O(n).

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