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"Quadratic forms on finite groups, and related topics", Charles Wall, 1963

Reviewed August 24, 2023

Citation: Wall, Charles Terence Clegg. "Quadratic forms on finite groups, and related topics." Topology 2.4 (1963): 281-298.

Web: https://www.sciencedirect.com/science/article/pii/0040938363900120

Tags: Mathematical, Abelian-anyons

This is one of the first detailed treatments of the theory of quadratic forms on abelian groups. In particular, a classification theorem is sketched.

One interesting subtelty is that quadratic forms are more complicated on abelian groups than odd groups and in particular are even more complicated on 2-groups of large order. This adds some philosophical complexity to the fact that quantum computation is typically based on Z2 (or larger 2-groups).

The theory of quadratic forms is very important for understanding abelian anyons, so this is a good reference to keep in mind.