On unitary groups associated to division algebras of degree three

Kathrin Maurischat

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arXiv · 1712.06821

On unitary groups associated to division algebras of degree three

Kathrin Maurischat

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Abstract

We show that the special unitary group associated to an involution of the second kind on a central division algebra of degree three does not contain hermitian or skew-hermitian elements. Especially, there are no reflections. For Albert's special cyclic presentation we show that the intersections of reasonable $S$-arithmetic subgroups with the two obvious maximal subfields consist of the trivial central elements.

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Kathrin Maurischat. 2017-12-19. On unitary groups associated to division algebras of degree three. https://arxiv.org/abs/1712.06821

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