English

Clifford Hopf gebra for two-dimensional space

Quantum Algebra 2007-05-23 v1 High Energy Physics - Theory

Abstract

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.

Cite

@article{arxiv.math/0011263,
  title  = {Clifford Hopf gebra for two-dimensional space},
  author = {Bertfried Fauser and Zbigniew Oziewicz},
  journal= {arXiv preprint arXiv:math/0011263},
  year   = {2007}
}

Comments

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