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.
Original language | English (US) |
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Pages (from-to) | 7944-7974 |
Number of pages | 31 |
Journal | International Mathematics Research Notices |
Volume | 2020 |
Issue number | 21 |
DOIs | |
State | Published - Nov 1 2020 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- General Mathematics