English

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 SS-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}
}