Mathematics of Clifford - a Maple package for Clifford and Graßmann algebras
نویسندگان
چکیده
منابع مشابه
Mathematics of CLIFFORD - A Maple Package for Clifford and Graßmann Algebras
CLIFFORD performs various computations in Graßmann and Clifford algebras. It can compute with quaternions, octonions, and matrices with entries in Cl(B) the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B. Two user-selectable algorithms for Clifford product are implemented: cmulNUM based on Chevalley’s recursive formula, and cmulRS based on non-recursive Rota-Stei...
متن کاملClifford and Graßmann Hopf algebras via the BIGEBRA package for Maple
Hopf algebraic structures will replace groups and group representations as the leading paradigm in forthcoming times. K-theory, co-homology, entanglement, statistics, representation categories, quantized or twisted structures as well as more geometric topics of invariant theory, e.g., the Graßmann-Cayley bracket algebra, are all covered by the Hopf algebraic framework. The new branch of experim...
متن کاملClifford and Graßmann Hopf algebras via the BIGEBRA package for Maple ( R ) ∗
Hopf algebraic structures will replace groups and group representations as the leading paradigm in forthcoming times. K -theory, co-homology, entanglement, statistics, representation categories, quantized or twisted structures as well as more geometric topics of invariant theory, e.g., the Graßmann-Cayley bracket algebra are all covered by the Hopf algebraic framework. The new branch of experim...
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CLIFFORD performs various computations in Graßmann and Clifford algebras. It can compute with quaternions, octonions, and matrices with entries in C (B) the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B. Two user-selectable algorithms for the Clifford product are implemented: cmulNUM based on Chevalley’s recursive formula, and cmulRS based on a non-recursive Rot...
متن کاملClifford 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: Advances in Applied Clifford Algebras
سال: 2005
ISSN: 0188-7009,1661-4909
DOI: 10.1007/s00006-005-0009-9