Ho, Wei; Satriano, Matthew Galois closures of non-commutative rings and an application to Hermitian representations. (English) Zbl 1469.16061 Int. Math. Res. Not. 2020, No. 21, 7944-7974 (2020). Summary: Galois closures of commutative rank \(n\) ring extensions were introduced by M. Bhargava and the first author [Camb. J. Math. 4, No. 1, 1–119 (2016; Zbl 1342.14074)]. 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. Cited in 1 Document MSC: 16S70 Extensions of associative rings by ideals 16S99 Associative rings and algebras arising under various constructions Keywords:Galois closures Citations:Zbl 1342.14074 PDFBibTeX XMLCite \textit{W. Ho} and \textit{M. Satriano}, Int. Math. Res. Not. 2020, No. 21, 7944--7974 (2020; Zbl 1469.16061) Full Text: DOI arXiv