Hecke algebras as subalgebras of Clifford geometric algebras of multivectors

Details Hecke algebras as subalgebras of Clifford geometric algebras of multivectors Hecke algebras as subalgebras of Clifford geometric algebras of multivectors

1997-10-16

arxiv.org/abs/q-alg/9710020v1

J. Phys. A: Math. Gen. 32 (1999) 1919-1936

Mathematics

Quantum Algebra

12p. 40kB, LaTeX, no figures, Bertfried.Fauser@uni-tuebingen.de

Scientific paper

10.1088/0305-4470/32/10/010

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.

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