A Note on the Eilenberg-Mac Lane Isomorphism for Quadratic Forms
Published: Jul 21, 2025
Last Updated: Jul 21, 2025
Authors:César Galindo
Abstract
We give an elementary proof of the Eilenberg-Mac Lane trace isomorphism between the third 2-abelian cohomology group and quadratic forms. Our approach yields explicit constructions and we characterize when quadratic forms can be expressed as traces of bilinear forms for arbitrary coefficient groups.