Selective orders in central simple algebras

Details Selective orders in central simple algebras Selective orders in central simple algebras

2012-04-11

arxiv.org/abs/1204.2526v1

Mathematics

Number Theory

Scientific paper

Let $B$ be a central simple algebra of degree $n$ over a number field $K$, and let $L/K$ be a field extension of degree $n$ which embeds in $B$. The question of which of the isomorphism classes of maximal orders in $B$ admit an embedding of an $\O_K$-suborder $\Omega$ of $\O_L$ is the question of selectivity of the order $\Omega$. In this paper we are concerned with algebras of degree $n \ge 3$, and continue the work of several authors to characterize the degree to which and conditions under which selectivity will occur. We take a local approach via the theory of affine buildings which provides explicit information about the structure of local embeddings, and leverage that information to produce a global characterization. We clarify that selectivity can never occur in an algebra which is a division algebra at a finite prime as well as construct representatives of the isomorphism classes of maximal orders which do admit embeddings of $\Omega$. An example of selectivity in an algebra with partial ramification is provided.

Affiliated with

Also associated with

No associations

Rating

Selective orders in central simple algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Selective orders in central simple algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Selective orders in central simple algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-717235