A generalization of the doubling construction for sums of squares identities

Chi Zhang; Hua-Lin Huang

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A generalization of the doubling construction for sums of squares identities

Chi Zhang 1, Hua-Lin Huang 2 * #

1.School of Mathematics, Shandong University, Jinan 250100, China

2.School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China

*Correspondence author

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Funding: SRFDP（No.20130131110001）

Opened online:17 May 2017

Accepted by: none

Citation: Chi Zhang, Hua-Lin Huang.A generalization of the doubling construction for sums of squares identities[OL]. [17 May 2017] http://en.paper.edu.cn/en_releasepaper/content/4733002

The doubling construction is a fast and important way to fill in the blanks of the solution table to the Hurwitz problem on sums of squares identities. By taking advantage of twisted group algebras over $Z_2^n$ and intercalate matrices, we generalize the doubling construction and obtain from any known admissible triple $[r,s,n]$ a series of new ones $[r+ ho(2^{m-1}),2^ms,2^mn]$ for all positive integer $m,$ where $ ho$ is the Hurwitz-Radon function.

Keywords:twisted group algebra; square identity; doubling construction; Hurwitz problem

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