Tensor Products of Cyclic Algebras of Degree 4 and their Kummer Subspaces

TL;DR

This paper determines the maximum dimension of Kummer spaces in the generic tensor product of cyclic algebras of degree 4, establishing a precise formula for their maximal size.

Contribution

It provides a new explicit formula for the maximal dimension of Kummer spaces in tensor products of cyclic algebras of degree 4.

Findings

Maximal dimension of Kummer spaces is 4n+1 in the generic tensor product of n cyclic algebras of degree 4.

The result generalizes previous bounds for specific cases.

The proof involves algebraic and combinatorial techniques.

Abstract

We prove that the maximal dimension of a Kummer space in the generic tensor product of $n$ cyclic algebras of degree 4 is $4 n+1$.