Grade free product formulae from Grassmann Hopf gebras
| dc.creator | Fauser, Bertfried | |
| dc.date | 2002-08-13 | |
| dc.date.accessioned | 2026-07-07T04:29:22Z | |
| dc.date.available | 2026-07-07T04:29:22Z | |
| dc.description | In the traditional approaches to Clifford algebras, the Clifford product is evaluated by recursive application of the product of a one-vector (span of the generators) on homogeneous i.e. sums of decomposable (Grassmann), multivectors and later extended by bilinearity. The Hestenesian 'dot' product, extending the one-vector scalar product, is even worse having exceptions for scalars and the need for applying grade operators at various times. Moreover, the multivector grade is not a generic Clifford algebra concept. The situation becomes even worse in geometric applications if a meet, join or contractions have to be calculated. Starting from a naturally graded Grassmann Hopf gebra, we derive general formulae for the products: meet and join, comeet and cojoin, left/right contraction, left/right cocontraction, Clifford and co-Clifford products. All these product formulae are valid for any grade and any inhomogeneous multivector factors in Clifford algebras of any bilinear form, including non-symmetric and degenerated forms. We derive the three well known Chevalley formulae as a specialization of our approach and will display co-Chevalley formulae. The Rota--Stein cliffordization is shown to be the generalization of Chevalley deformation. Our product formulae are based on invariant theory and are not tied to representations/matrices and are highly computationally effective. The method is applicable to symplectic Clifford algebras too. | |
| dc.description | uses pstricks for tangle pictures, 24p + toc,index; pdf file may be corrupt, see http://kaluza.physik.uni-konstanz.de/~fauser/ | |
| dc.identifier | https://arxiv.org/abs/math-ph/0208018 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0208018 | |
| dc.identifier | in "Clifford Algebras and their Applications in Mathematical Physics" eds. R. Abłamowicz, J. Ryan, Birkhäuser Boston 2003, pp. 281-306 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/57126 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Rings and Algebras | |
| dc.subject | 16W30; 15A66 | |
| dc.title | Grade free product formulae from Grassmann Hopf gebras | |
| dc.type | text |