Galois closures of non-commutative rings and an application to Hermitian representations

2018/06/21 by Wei Ho, Matthew Satriano, Ho, Wei +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.AG #math.RA #math.RT

paper · pdf · doi:10.48550/arxiv.1806.08345

20 pages, comments welcome!

arxiv created 2018/06/21 · openalex publication_date 2018/06/21 · arxiv updated 2018/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Galois closures of commutative rank n ring extensions were introduced by Bhargava and the second author. In this paper, we generalize the construction to the case of non-commutative rings. We show that non-commutative Galois closures commute with base change and satisfy a product formula. As an application, we give a uniform construction of many of the representations arising in arithmetic invariant theory, including many Vinberg representations.

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