On alphabetic presentations of Clifford algebras and their possible applications
نویسندگان
چکیده
منابع مشابه
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 define groups constructed from ‘Clifford numbers’ and use them to represent rotations in a Euclidean space. É. Cartan discovered representations of the Lie algebras son(C) and son(R), n > 2, that do ...
متن کاملNotes on Weyl–Clifford algebras
Here is discussed generalization of Clifford algebras, l-dimensional Weyl–Clifford algebras T(n, l) with n generators tk satisfying equation ∑n k=1 aktk )l = ∑n k=1 (ak) . It is originated from two basic and well known constructions: representation of Clifford algebras via tensor products of Pauli matrices together with extension for l > 2 using Weyl commutation relations. Presentation of such ...
متن کاملBasic Calculations on Clifford Algebras
Clifford algebras are important structures in Geometric Algebra and Quantum Mechanics. They have allowed a formalization of the primitive operators in Quantum Theory. The algebras are built over vector spaces with dimension a power of 2 with addition and multiplication being effectively computable relative to the computability of their own spaces. Here we emphasize the algorithmic notions of th...
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Clifford Algebras and Graphs
I show how to associate a Clifford algebra to a graph. I describe the structure of these Clifford graph algebras and provide many examples and pictures. I describe which graphs correspond to isomorphic Clifford algebras and also discuss other related sets of graphs. This construction can be used to build models of representations of simplylaced compact Lie groups. 1 Clifford Algebras Let A be a...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2009
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.3272001