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1996 | 37 | 1 | 315-325
Tytuł artykułu

Spinors in braided geometry

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Języki publikacji
EN
Abstrakty
EN
Let V be a ℂ-space, $σ ∈ End(V^{⊗2})$ be a pre-braid operator and let $F ∈ lin(V^{⊗2},ℂ).$ This paper offers a sufficient condition on (σ,F) that there exists a Clifford algebra Cl(V,σ,F) as the Chevalley F-dependent deformation of an exterior algebra $Cl(V,σ,0) ≡ V^{∧}(σ)$. If $σ ≠ σ^{-1}$ and F is non-degenerate then F is not a σ-morphism in σ-braided monoidal category. A spinor representation as a left Cl(V,σ,F)-module is identified with an exterior algebra over F-isotropic ℂ-subspace of V. We give a sufficient condition on braid σ that the spinor representation is faithful and irreducible.
Słowa kluczowe
Rocznik
Tom
37
Numer
1
Strony
315-325
Opis fizyczny
Daty
wydano
1996
Twórcy
  • Instituto de Matematicas, UNAM, Area de la Investigacion Cientifica, Circuito Exterior, Ciudad Universitaria, México DF, CP 04510 México
  • Facultad de Estudios Superiores Cuautitlan, UNAM, Apartado Postal , #25 Cuautitlan Izcalli, CP 54700, México
Bibliografia
  • [1] R. Bautista, A. Criscuolo, M. Đurđević, M. Rosenbaum and J.D. Vergara, Quantum Clifford algebras from spinor representations, J. Math. Phys. (1996), to appear.
  • [2] N. Bourbaki, Algébre, chap. 9: formes sesquilinéaries et formes quadratiques, Paris, Hermann, 1959.
  • [3] É. Cartan, The Theory of Spinors, Dover Pub., New York, 1966.
  • [4] A. Crumeyrolle, Orthogonal and Symplectic Clifford Algebras. Spinor Structures, Mathematics and its Applications vol. 57, Kluwer Academic Publishers, 1990.
  • [5] M. Đurđević, Braided Clifford algebras as braided quantum groups, Adv. Apppl. Cliff. Algebras 4 (2) (1994), 145-156.
  • [6] M. Đurđević, Generalized braided quantum groups, Isr. J. Math. (1996), to appear.
  • [7] T. Hayashi, Q-analogues of Clifford and Weyl algebras - spinor and oscilator representations of quantum enveloping algebras, Commun. Math. Phys. 127 (1990), 129-144.
  • [8] S. Majid, Braided groups and algebraic quantum field theories, Lett. Math. Phys. 22 (1991), 167-176.
  • [9] S. Majid, Braided groups, J. Pure and Applied Algebra 86 (1993), 187-221.
  • [10] S. Majid, Transmutation theory and rank for quantum braided groups, Math. Proc. Camb. Phil. Soc. 113 (1993), 45-70.
  • [11] S. Majid, Free braided differential calculus, braided binomial theorem and the braided exponential map, J. Math. Phys. 34 (1993), 4843-4856.
  • [12] S. Majid, Foundations of Quantum Group Theory, Cambridge University Press 1995.
  • [13] Z. Oziewicz, E. Paal and J. Różański, Derivations in braided geometry, Acta Physica Polonica B 26 (7) (1995), 1253-1273.
  • [14] Z. Oziewicz, Clifford algebra for Hecke braid, in: Clifford Algebras and Spinor Structures, R. Ablamowicz and P. Lounesto (ed.), Mathematics and Its Applications vol. 321, Kluwer Academic Publishers, Dordrecht 1995, pp. 397-411.
  • [15] S. Shnider and S. Sternberg, Quantum Groups, from coalgebras to Drinfeld algebras a guided tour, International Press Incorporated, Boston, 1993.
  • [16] M. E. Sweedler, Hopf Algebras, Benjamin, Inc., New York, 1969.
  • [17] S. L. Woronowicz, Differential calculus on compact matrix pseudogroups (quantum groups), Commun. Math. Phys. 122 (1989), 125-170.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv37i1p315bwm
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