Hecke algebras as subalgebras of Clifford geometric algebras of multivectors

Abstract

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(K^{2n},B), we proof that theses elements generate the Hecke algebra H_{K}(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.