We study briefly some properties of real Clifford algebras and identify them as matrix algebras. We then show that the representation space on which Clifford algebras act are spinors and we study in details matrix representations. The precise structure of these matrices gives rise to the type of spinors one is able to construct in a given space-time dimension: Majorana or Weyl. Properties of spinors are also studied. We finally show how Clifford algebras enable us to construct supersymmetric extensions of the Poincaré algebra. A special attention to the four, ten and eleven-dimensional space-times is given. We then study the representations of the considered supersymmetric algebras and show that representation spaces contain an equal number of bosons and fermions. Supersymmetry turns out to be a symmetry which mixes non-trivially the bosons and the fermions since one multiplet contains bosons and fermions together. We also show how supersymmetry in four and ten dimensions are related to eleven dimensional supersymmetry by compactification or dimensional reduction.

Michel Rausch de Traubenberg

Advances in Applied Clifford Algebras

ADVANCES IN APPLIED CLIFFORD ALGEBRAS (AACA) 在 CLIFFORD 代数及其在数学、物理、工程和相关领域的其他分支中的应用领域发表高质量的同行评审研究论文以及说明性和调查性文章。该杂志确保快速出版，分为六个部分：分析、微分几何和狄拉克算子、数学结构、理论和数学物理、应用和书评。

The journal "Advances in Applied Clifford Algebras" focuses on Clifford algebras and their applications in mathematics, physics, engineering, and related fields. It publishes high-quality peer-reviewed research papers, as well as expository and survey articles, ensuring rapid publication. The journal is divided into six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.

《Advances in Applied Clifford Algebras》期刊专注于克利福德代数及其在数学、物理、工程及相关领域的应用。该期刊发表高质量的同行评审研究论文，以及说明性和调查性文章，确保快速出版。期刊内容分为六个部分：分析、微分几何与狄拉克算子、数学结构、理论与数学物理、应用以及书评。

Category	Quartile
数学	2
数学, 应用数学	2
数学, 物理数学物理	2

Clifford Algebras in Physics

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Journal Info

Category	Quartile
PHYSICS, MATHEMATICAL	3