Kummer Subspaces of Tensor Products of Cyclic Algebras

2014/05/01 by Adam Chapman, Chapman, Adam
Mathematics · #05C38 #16K20 (Primary) #16W60 (Secondary) #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:05C38 #msc:16K20 #msc:16W60

paper · pdf · doi:10.48550/arxiv.1405.0188

8 pages

arxiv created 2014/05/01 · arxiv updated 2014/05/02

Abstract

We discuss the Kummer subspaces of tensor products of cyclic algebras, focusing mainly on the case of cyclic algebras of degree 3. We present a family of maximal spaces in the general case, classify all the monomial spaces in the case of tensor products of cyclic algebras of degree 3 using graph theory, and provide an upper bound for the dimension in the generic tensor product of cyclic algebras of degree 3.

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