A Generalized Composition of Quadratic Forms based on Quadratic Pairs
Roland L\"otscher
TL;DR
This paper extends the concept of hermitian compositions to quadratic pairs, providing a generalized framework and identifying minimal composition degrees for various quadratic pairs.
Contribution
It introduces a generalized composition concept based on quadratic pairs, expanding the algebraic understanding beyond quadratic spaces that represent 1.
Findings
Characterization of hermitian compositions via even Clifford algebra
Definition of generalized compositions based on quadratic pairs
Determination of minimal composition degrees for quadratic pairs
Abstract
For quadratic spaces which represent 1 there is a characterization of hermitian compositions in the language of algebras-with-involutions using the even Clifford algebra. We extend this notion to define a generalized composition based on quadratic pairs and determine the degrees of minimal compositions for any given quadratic pair.
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Taxonomy
TopicsAdvanced Algebra and Geometry · Advanced Topics in Algebra · Algebraic Geometry and Number Theory