Clifford Hopf gebra for two-dimensional space

Details Clifford Hopf gebra for two-dimensional space Clifford Hopf gebra for two-dimensional space

2000-11-30

arxiv.org/abs/math/0011263v1

Miscellanea Algebraicae Vol 5, No 2:31-42, 2001

Mathematics

Quantum Algebra

14 pages, 8 eps-figure, submitted to `Miscellanea Algebraica' Kielce, Poland

Scientific paper

A Clifford algebra Cl(V,\eta\in V^*\otimes V^*) jointly with a Clifford cogebra Cl(V,\xi\in V\otimes V) is said to be a Clifford biconvolution Cl(\eta,\xi). We show that a Clifford biconvolution for dim_R Cl=4 does possess an antipode iff det(id-\xi\circ\eta)\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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