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1997 | 40 | 1 | 99-110
Tytuł artykułu

Braided modules and reflection equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We introduce a representation theory of q-Lie algebras defined earlier in [DG1], [DG2], formulated in terms of braided modules. We also discuss other ways to define Lie algebra-like objects related to quantum groups, in particular, those based on the so-called reflection equations. We also investigate the truncated tensor product of braided modules.
Słowa kluczowe
Rocznik
Tom
40
Numer
1
Strony
99-110
Opis fizyczny
Daty
wydano
1997
Twórcy
  • ISTV, Université de Valenciennes, 59304 Valenciennes, France
Bibliografia
  • [BG] A. Braverman, D. Gaitsgory, Poincaré-Birkhoff-Witt theorem for quadratic algebras of Koszul type, hep-th/9411113.
  • [DH] G. Delius, A. Hüffmann, On quantum algebras and quantum root systems, q-alg/9506017.
  • [DG1] J. Donin, D. Gurevich, Braiding of the Lie algebra $sl(2)$, Amer. Math. Soc. Transl. (2) 167 (1995), pp. 23-36.
  • [DG2] J. Donin, D. Gurevich, Quantum orbits of R-matrix type, Lett. Math. Phys. 35 (1995), pp. 263-276.
  • [DGR] J. Donin, D. Gurevich, V. Rubtsov, Quantum hyperboloid and braided modules, q-alg/9511014.
  • [G] D. Gurevich, Algebraic aspects of the quantum Yang-Baxter equation, Leningrad Math.J. 2 (1991), pp. 801-828.
  • [GP] D. Gurevich, D. Panyushev, On Poisson pairs associated to modified R-matrices, Duke Math. J. 73 (1994), pp.249-255.
  • [GR] D. Gurevich, V. Rubtsov, Quantization of Poisson pencils and generalized Lie algebras, Teor. i Mat. Phys. 103 (1995), pp. 476-488.
  • [I1] A. Isaev, Interrelation between Quantum Groups and Reflection Equation (Braided) Algebras, Lett. Math. Phys. 34 (1995), pp. 333-341.
  • [I2] A. Isaev, Quantum Groups and Yang-Baxter Equation, Phys. Part. Nucl. 26 (1995) n 5, pp. 501-526 (Russian).
  • [IP1] A. Isaev, P. Pyatov, $GL_q(N)$-covariant quantum algebras and covariant differential calculus, Phys. Let. A 179 (1993), pp.81-90.
  • [IP2] A. Isaev, P. Pyatov, Covariant differential complex on quantum linear groups, J. Phys. A: Math. Gen. 28 (1995), pp. 2227-2246.
  • [KSS] P. Kulish, R. Sasaki, C. Schwiebert, Constant Solution of Reflection Equations and Quantum Groups, hep-th/9205039.
  • [LS] V. Lyubashenko, A. Sudbery, Quantum Lie algebras of type $A_n$, q-alg/9510004.
  • [M] Sh. Majid, Quantum and braided Lie algebras, JGP 13 (1994), pp.307-356.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv40z1p99bwm
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