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arXiv · 2104.12529

Generation of Local Unitary Groups

Simon Brandhorst·Tommy Hofmann·Sven Manthe
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Abstract

Let $E$ be a two-dimensional \'etale algebra over a non-Archimedean local field $K$ of characteristic zero. We show that the unitary group of a non-degenerate hermitian lattice over $E$ is generated by symmetries and rescaled Eichler isometries. In the appendix we show that unless $E/K$ is a ramified dyadic field extension and the residue field has two elements, symmetries suffice.

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Simon Brandhorst, Tommy Hofmann, Sven Manthe. 2021-04-26. Generation of Local Unitary Groups. https://doi.org/10.1016/j.jalgebra.2022.07.007

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