Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
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
Czasopismo
Rocznik
Tom
Numer
Strony
99-110
Opis fizyczny
Daty
wydano
1997
Twórcy
autor
- 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
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