Galois Closures of Non-commutative Rings and an Application to Hermitian Representations. (3rd October 2018)

• Record Type: Journal Article
• Authors: Ho, Wei; Satriano, Matthew
• Is Part Of: International mathematics research notices. Volume 2020:Number 21(2020)
• Page Start: 7944
• Page End: 7974
• Publication Date: 2018-10-03
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rny231
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: Galois closures of commutative rank $n$ ring extensions were introduced by Bhargava and the 2nd author. In this paper, we generalize the construction to the case of non-commutative rings. We show that noncommutative 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.