论文标题
克利福德代数的建筑
A Construction for Clifford Algebras
论文作者
论文摘要
本文致力于Zbigniew Oziewicz的记忆，这是他在科学和数学的搜索中的慷慨，智力和强度。该论文始于基本的结构，该结构从归纳性的Clifford代数产生，首先是基本代数A，该代数A是关联的，并且有涉及。这种结构是Cayley-Dickson结构的类似物，该结构从实际数字开始产生复数，四元组和八元。我们的基本结构总是会产生联想代数，并且可以无限期地迭代。我们将基本结构概括为G组在代数A上作用的理论结构，并展示该组理论结构与基质代数有关。然后，该论文将该代数的应用集中在Dirac方程和Majoraana-Dirac方程式上。
This paper is dedicated to the memory of Zbigniew Oziewicz, to his generosity, intelligence and intensity in the search that is science and mathematics. The paper begins with a basic construction that produces Clifford algebras inductively, starting with a base algebra A that is associative and has an involution. This construction is an analog of the Cayley-Dickson Construction that produces the complex numbers, quaternions and octonions starting from the real numbers. Our basic construction always produces associative algebras and can be iterated an indefinite number of times. We generalize the basic construction to a group theoretic construction where a group G acts on the algebra A, and show how this group theoretic construction is related to matrix algebras. The paper then concentrates on applications of this algebra to the Dirac Equation and the Majorana-Dirac Equation.
