• Corpus ID: 195699879

Expository paper on Clifford algebras ,representations , and the octonion algebra

@article{Suarez2019ExpositoryPO,
  title={Expository paper on Clifford algebras ,representations , and the octonion algebra},
  author={Ricardo Suarez},
  journal={arXiv: Representation Theory},
  year={2019}
}
  • R. Suarez
  • Published 27 June 2019
  • Mathematics
  • arXiv: Representation Theory
This paper is meant to be an informative introduction to spinor representations of Clifford algebras. In this paper we will have a look at Clifford algebras and the octonion algebra. We begin the paper looking at the quaternion algebra $\mathbb{H}$ and basic properties that relate Clifford algebras and the well know Pin and Spin groups. We then will look at generalized spinor representations of Clifford algebras, along with many examples. We conclude the paper looking at the octonion algebra… 
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References

SHOWING 1-10 OF 26 REFERENCES

Cli ord Algebras and the Classical Groups

The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper…

Clifford Algebras and Lie Theory

Preface.- Conventions.- List of Symbols.- 1 Symmetric bilinear forms.- 2 Clifford algebras.- 3 The spin representation.- 4 Covariant and contravariant spinors.- 5 Enveloping algebras.- 6 Weil…

CLIFFORD ALGEBRAS AND THEIR REPRESENTATIONS

Introductory and historical remarks Clifford (1878) introduced his ‘geometric algebras’ as a generalization of Grassmann algebras, complex numbers and quaternions. Lipschitz (1886) was the first to…

Clifford Algebras: An Introduction

Introduction Part I. The Algebraic Environment: 1. Groups and vector spaces 2. Algebras, representations and modules 3. Multilinear algebra Part II. Quadratic Forms and Clifford Algebras: 4.…

A New Representation for Spinors in Real Clifford Algebras

A new representation of a real Clifford algebra by itself is presented, which does not use onesided minimal ideals. This generalizes the “operator form” for Dirac spinors introduced by D. Hestenes.…

Spinor representations of Clifford algebras: a symbolic approach

On the Structure Theorem of Clifford Algebras

In this paper, theory and construction of spinor representations of real Clifford algebras $\cl_{p,q}$ in minimal left ideals are reviewed. Connection with a general theory of semisimple rings is…

Canonical bases for real representations of Clifford algebras

Lectures on Clifford (geometric) algebras and applications

Preface (Rafal Ablamowicz and Garret Sobczyk) * Lecture 1: Introduction to Clifford Algebras (Pertti Lounesto) * 1.1 Introduction * 1.2 Clifford algebra of the Euclidean plane * 1.3 Quaternions * 1.4…

Lie Groups: An Introduction through Linear Groups

Lie Groups is intended as an introduction to the theory of Lie groups and their representations at the advanced undergraduate or beginning graduate level. It covers the essentials of the subject…