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1997 | 40 | 1 | 91-97
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Introduction to quantum Lie algebras

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras $U_h(g)$. The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. The recent general results about quantum Lie algebras are introduced with the help of the explicit example of $(sl_2)_h$.
Słowa kluczowe
Rocznik
Tom
40
Numer
1
Strony
91-97
Opis fizyczny
Daty
wydano
1997
Twórcy
  • Department of Physics, University of Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany
Bibliografia
  • [1] Dri V. G. Drinfel'd, Hopf algebras and the quantum Yang-Baxter equation, Sov. Math. Dokl. 32 (1985) 254.
  • [2] Jim M. Jimbo, A q-Difference Analogue of U(g) and the Yang-Baxter Equation, Lett. Math. Phys. 10 (1985) 63.
  • [3] G. W. Delius, A. Hüffmann, On Quantum Lie Algebras and Quantum Root Systems, q-alg/9506017, J. Phys. A. 29 (1996) 1703.
  • [4] G. W. Delius, M. D. Gould, Quantum Lie Algebras, their existence, uniqueness and q-antisymmetry, KCL-TH-96-05, q-alg/9605025, Commun. Math. Phys. (in print).
  • [5] S. L. Woronowicz, Differential Calculus on Compact Matrix Pseudogroups (Quantum Groups), Comm. Math. Phys. 122 (1989) 125.
  • [6] P. Aschieri, L. Castellani, An introduction to noncommutative differential geometry on quantum groups, Int. J. Mod. Phys. A8 (1993) 1667
  • D. Bernard, Quantum Lie Algebras and Differential Calculus on Quantum Groups, Prog. Theo. Phys. Suppl. 102 (1990) 49
  • B. Jurco, Differential Calculus on Quantized Simple Lie Groups, Lett. Math. Phys. 22 (1991) 177
  • P. Schupp, P. Watts, B. Zumino, Bicovariant Quantum Algebras and Quantum Lie Algebras, Commun. Math. Phys. 157 (1993) 305
  • P. Schupp, Quantum Groups, Non-Commutative Differential Geometry and Applications, hep-th/9312075 (1993)
  • K. Schmüdgen, A. Schüler, Classification of Bicovariant Differential Calculi on Quantum Groups of Type A, B, C and D, Comm. Math. Phys. 107 (1995) 635
  • A. Sudbery, Quantum Lie Algebras of Type $A_n$, q-alg/9510004.
  • [7] Andrew V. Chari, A. Pressley, A Guide to Quantum Groups, Cambridge University Press (1994).
  • [8] G.W. Delius, M.D. Gould, A. Hüffmann, Y.-Z. Zhang, Quantum Lie algebras associated to $U_q(gl_n)$ and $U_q(sl_n)$, q-alg/9508013.
  • [9] V. Lyubashenko and A. Sudbery, Quantum Lie algebras of type A(N), q-alg/9510004.
  • [10] World Wide Web, http:/www.mth.kcl.ac.uk/~delius/q-lie.html.
Typ dokumentu
Bibliografia
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