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.

12p. 40kB, LaTeX, no figures, [email protected]

References in corpus (4)

• On an easy transition from operator dynamics to generating functionals by Clifford algebras
• Positronium as an example of algebraic composite calculations
• Clifford Algebraic Remark on the Mandelbrot Set of Two--Component Number Systems
• On the relation of Clifford-Lipschitz groups to q-symmetric groups

Cited by in corpus (10)

• Bilinear Covariants and Spinor Fields Duality in Quantum Clifford Algebras
• On the Hopf algebraic origin of Wick normal-ordering
• A Treatise on Quantum Clifford Algebras
• On the transposition anti-involution in real Clifford algebras I: The transposition map
• Z_2-gradings of Clifford algebras and multivector structures
• Clifford geometric parameterization of inequivalent vacua
• On the equivalence of Daviau's space Clifford algebraic, Hestenes' and Parra's formulations of (real) Dirac theory
• On the relation of Manin's quantum plane and quantum Clifford algebras
• Hecke Algebras, SVD, and Other Computational Examples with {\sc CLIFFORD}
• Hecke Algebra Representations in Ideals Generated by q-Young Clifford Idempotents