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A Direct Approach to Noncrossed Product Division Algebras.

Fri, 09/09/2011 - 15:01 — SomNambul
Authors: Timo Hanke
Subjects: Rings and Algebras
link: http://arxiv.org/abs/1109.1580
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.

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