On unitary groups associated to division algebras of degree three
Number Theory
2017-12-20 v1
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 -arithmetic subgroups with the two obvious maximal subfields consist of the trivial central elements.
Keywords
Cite
@article{arxiv.1712.06821,
title = {On unitary groups associated to division algebras of degree three},
author = {Kathrin Maurischat},
journal= {arXiv preprint arXiv:1712.06821},
year = {2017}
}