Clifford Hopf gebra for two-dimensional space

2000/11/30 by Bertfried Fauser, Zbigniew Oziewicz
Mathematics · Physics and Astronomy · #math.QA #hep-th #msc:15A66 #msc:16W30

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published as Miscellanea Algebraicae Vol 5, No 2:31-42, 2001 · 14 pages, 8 eps-figure, submitted to `Miscellanea Algebraica' Kielce, Poland

arxiv created 2000/11/30 · arxiv updated 2009/11/30

Abstract

A Clifford algebra Cl(V,η∈ V^*⊗ V^*) jointly with a Clifford cogebra Cl(V,ξ∈ V⊗ V) is said to be a Clifford biconvolution Cl(η,ξ). We show that a Clifford biconvolution for dim_R Cl=4 does possess an antipode iff det(id-ξ∘η)≠ 0. An antipodal Clifford biconvolution is said to be a Clifford Hopf gebra. We study the Clifford Hopf gebra and examples of antipode less Clifford bigebras including the Grassmann case.

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