Hecke algebras as subalgebras of Clifford geometric algebras of multivectors

Clifford geometric algebras of multivectors are introduced which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in Cl(IK, B), we proof that theses elements generate the Hecke algebra HIK(n + 1, q) if the bilinear form B is chosen appropriately. This shows, that q-quantization can be generated by Clifford multivector objects which describe usually composite entities. This contrasts current approaches which give deformed versions of Clifford algebras by deforming the one-vector variables. Our example shows, that it is not evident from a mathematical point of view, that q-deformation is in any sense more elementary than the undeformed structure. PACS: 02.10; 02.40; 05.30; 11.10 MSC1991: 15A66; 17B37; 81R50