Kummer Subspaces of Tensor Products of Cyclic Algebras

TL;DR

This paper investigates the structure of Kummer subspaces within tensor products of cyclic algebras, especially degree 3, providing classifications, bounds, and new maximal space constructions.

Contribution

It introduces a classification of monomial Kummer spaces for degree 3 cyclic algebras using graph theory and constructs a family of maximal spaces.

Findings

Classified all monomial Kummer spaces for degree 3

Provided an upper bound for the dimension of these spaces

Constructed a family of maximal Kummer spaces

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.