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Galois closures of non-commutative rings and an application to Hermitian representations. (English) Zbl 1469.16061

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.

MSC:

16S70 Extensions of associative rings by ideals
16S99 Associative rings and algebras arising under various constructions

Keywords:

Galois closures

Citations:

Zbl 1342.14074
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