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arXiv · 1806.08345

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

Wei Ho·Matthew Satriano
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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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Wei Ho, Matthew Satriano. 2018-06-21. Galois closures of non-commutative rings and an application to Hermitian representations. https://arxiv.org/abs/1806.08345

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