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Clifford Hopf gebra for two-dimensional space

Bertfried Fauser·Zbigniew Oziewicz
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Abstract

A Clifford algebra Cl(V,η\in V^*\otimes V^*) jointly with a Clifford cogebra Cl(V,ξ\in V\otimes 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\circη)\neq 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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Bertfried Fauser, Zbigniew Oziewicz. 2000-11-30. Clifford Hopf gebra for two-dimensional space. https://arxiv.org/abs/math/0011263

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