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Quantum algebras

I. - Basic algebraic and topological structures

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Il Nuovo Cimento B (1971-1996)

Summary

Quantum algebras are the universal algebras, associated to a finite-dimensional vector space and its endomorphisms. The Fermi or Bose statistics of a quantum algebra reflects the (anti-)symmetry of the basic-space dual product. The relation to the universal enveloping algebra of the basic endomorphisms and to the dual-product Clifford algebra is discussed together with its invariants. According to the Abelian or non-Abelian basic-space endomorphism algebra, it carries two different trace-induced linear forms-the Fock and the Heisenberg form, respectively. With a quantum algebra conjugation,e.g. connected with a-not necessarily Euclidean unitary-time representation, quantum algebras have an inner product and, in the case of a positive conjugation, a Hilbert space of Fock type for the Abelian and of Heisenberg type for the non-Abelian case.

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Authors and Affiliations

  1. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, P.O. Box 401212, Munich, Germany

    H. Saller

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  1. H. Saller
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Saller, H. Quantum algebras. Nuov Cim B 108, 603–630 (1993). https://doi.org/10.1007/BF02826997

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  • DOI: https://doi.org/10.1007/BF02826997

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