A Direct Approach to Noncrossed Product Division Algebras
Rings and Algebras
2011-09-09 v1 Number Theory
Abstract
A valuation theoretic approach is presented that directly leads to division algebras that are noncrossed products (instead of, e.g., describing Brauer classes of noncrossed products in an abstract manner). While this feature is shared by Amitsur's original construction, the new approach works over small fields. It is further demonstrated how it can be used to obtain very explicit examples of noncrossed products in the form of iterated twisted function fields over division algebras over global fields. The examples allow even to write down structure constants of noncrossed products.
Keywords
Cite
@article{arxiv.1109.1580,
title = {A Direct Approach to Noncrossed Product Division Algebras},
author = {Timo Hanke},
journal= {arXiv preprint arXiv:1109.1580},
year = {2011}
}
Comments
Dissertation, Univ. Potsdam, Naturwissenschaftliche Fakult\"at, xii, 64 p