\'Algebras y grupos de Clifford, espinores algebraicos y aplicaciones a la f\'isica

TL;DR

This paper introduces Clifford algebras, groups, and spinors using algebraic methods, exploring their relation to quadratic forms and applications in physics.

Contribution

It provides a comprehensive algebraic framework for Clifford algebras, groups, and spinors, connecting them to quadratic spaces and physical applications.

Findings

Defined Clifford, Pin, and Spin groups and their relations.

Constructed algebraic spinors as minimal left ideals.

Discussed applications of spinors in physics.

Abstract

In these notes we introduce the Clifford algebra of a quadratic space using techniques from universal algebra and algebraic theory of quadratic forms. We also define the Clifford, Pin and Spin groups associated to the algebra, and study how they relate to the isommetry group of the original quadratic space. Lastly we introduce the algebraic spinors space as a minimal left ideal (equivalently an irreducible representation) over the Clifford algebra, and mention its application in physics.