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Kummer subspaces of tensor products of cyclic algebras


Author: Adam Chapman
Journal: Proc. Amer. Math. Soc. 145 (2017), 4247-4253
MSC (2010): Primary 16K20; Secondary 05C38, 16W60
DOI: https://doi.org/10.1090/proc/13599
Published electronically: April 6, 2017
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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 Kummer spaces in any tensor product of cyclic algebras of prime degree, classify all the monomial Kummer spaces in tensor products of cyclic algebras of degree 3, and provide an upper bound for the dimension of Kummer spaces in the generic tensor product of cyclic algebras of degree 3.


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Additional Information

Adam Chapman
Affiliation: Department of Computer Science, Tel-Hai Academic College, Upper Galilee, 12208 Israel
Email: adam1chapman@yahoo.com

DOI: https://doi.org/10.1090/proc/13599
Keywords: Central simple algebras, cyclic algebras, Kummer spaces, generic algebras, graphs
Received by editor(s): May 5, 2014
Received by editor(s) in revised form: October 18, 2016, and November 22, 2016
Published electronically: April 6, 2017
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2017 American Mathematical Society