Abstract
Woronowicz in 1989 introduced a graded exterior algebra for arbitrary braid operator. In the present paper we give necessary and sufficient conditions between scalar product and braid operator that exists a Clifford algebra and that exists the Chevalley deformation of Woronowicz’s exterior algebra. In particular a quantum Clifford and Weyl algebras for a Hecke braid are isomorphic to Chevalley’s deformations of an algebras of quantum fermions and of quantum bosons respectively. We discuss deformation versus quantization, braided monoidal category, inner product for arbitrary braid and the Crumeyrolle algebra isomorphisms.
This paper is in final form and no version of it will be submitted for publication elsewhere.
Research partially supported by State Committee of Scientific Research, Poland, KBN grant # 2 P302 023 07.
The paper was written in Centro de Investigaciones Teoricas, Facultad de Estudios Superiores Cuautitlán, UNAM, Apartado Postal # 25, CP 54700 Cuautitlán Izcalli, Estado de México, (oziewicz@servidor.unam.mx).
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References
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Oziewicz, Z. (1995). Clifford Algebra for Hecke Braid. In: Ablamowicz, R., Lounesto, P. (eds) Clifford Algebras and Spinor Structures. Mathematics and Its Applications, vol 321. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8422-7_26
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DOI: https://doi.org/10.1007/978-94-015-8422-7_26
Publisher Name: Springer, Dordrecht
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