dorsal/arxiv
View SchemaHecke algebras as subalgebras of Clifford geometric algebras of multivectors
| Authors | Bertfried Fauser |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9710020 |
| URL | https://arxiv.org/abs/q-alg/9710020 |
| DOI | 10.1088/0305-4470/32/10/010 |
| Journal | J. Phys. A: Math. Gen. 32 (1999) 1919-1936 |
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.
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"abstract": "Clifford geometric algebras of multivectors are introduced which exhibit a\nbilinear form which is not necessarily symmetric. Looking at a subset of\nbi-vectors in CL(K^{2n},B), we proof that theses elements generate the Hecke\nalgebra H_{K}(n+1,q) if the bilinear form B is chosen appropriately. This\nshows, that q-quantization can be generated by Clifford multivector objects\nwhich describe usually composite entities. This contrasts current approaches\nwhich give deformed versions of Clifford algebras by deforming the one-vector\nvariables. Our example shows, that it is not evident from a mathematical point\nof view, that q-deformation is in any sense more elementary than the undeformed\nstructure.",
"arxiv_id": "q-alg/9710020",
"authors": [
"Bertfried Fauser"
],
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"q-alg",
"math.QA"
],
"doi": "10.1088/0305-4470/32/10/010",
"journal_ref": "J. Phys. A: Math. Gen. 32 (1999) 1919-1936",
"title": "Hecke algebras as subalgebras of Clifford geometric algebras of multivectors",
"url": "https://arxiv.org/abs/q-alg/9710020"
},
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