# Braided modules and reflection equations

Banach Center Publications (1997)

- Volume: 40, Issue: 1, page 99-110
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topGurevich, Dimitri. "Braided modules and reflection equations." Banach Center Publications 40.1 (1997): 99-110. <http://eudml.org/doc/252217>.

@article{Gurevich1997,

abstract = {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.},

author = {Gurevich, Dimitri},

journal = {Banach Center Publications},

keywords = {braided Lie algebra; representation; -Lie algebras; quantum groups; reflection equations; truncated tensor product; braided modules},

language = {eng},

number = {1},

pages = {99-110},

title = {Braided modules and reflection equations},

url = {http://eudml.org/doc/252217},

volume = {40},

year = {1997},

}

TY - JOUR

AU - Gurevich, Dimitri

TI - Braided modules and reflection equations

JO - Banach Center Publications

PY - 1997

VL - 40

IS - 1

SP - 99

EP - 110

AB - 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.

LA - eng

KW - braided Lie algebra; representation; -Lie algebras; quantum groups; reflection equations; truncated tensor product; braided modules

UR - http://eudml.org/doc/252217

ER -

## References

top- [BG] A. Braverman, D. Gaitsgory, Poincaré-Birkhoff-Witt theorem for quadratic algebras of Koszul type, hep-th/9411113. Zbl0860.17002
- [DH] G. Delius, A. Hüffmann, On quantum algebras and quantum root systems, q-alg/9506017. Zbl0916.17011
- [DG1] J. Donin, D. Gurevich, Braiding of the Lie algebra $sl\left(2\right)$, Amer. Math. Soc. Transl. (2) 167 (1995), pp. 23-36. Zbl0853.17009
- [DG2] J. Donin, D. Gurevich, Quantum orbits of R-matrix type, Lett. Math. Phys. 35 (1995), pp. 263-276. Zbl0853.17010
- [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. Zbl0728.17012
- [GP] D. Gurevich, D. Panyushev, On Poisson pairs associated to modified R-matrices, Duke Math. J. 73 (1994), pp.249-255. Zbl0824.58022
- [GR] D. Gurevich, V. Rubtsov, Quantization of Poisson pencils and generalized Lie algebras, Teor. i Mat. Phys. 103 (1995), pp. 476-488. Zbl0855.58032
- [I1] A. Isaev, Interrelation between Quantum Groups and Reflection Equation (Braided) Algebras, Lett. Math. Phys. 34 (1995), pp. 333-341. Zbl0878.17012
- [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, $G{L}_{q}\left(N\right)$-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. Zbl0860.58003
- [KSS] P. Kulish, R. Sasaki, C. Schwiebert, Constant Solution of Reflection Equations and Quantum Groups, hep-th/9205039. Zbl0799.17010
- [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. Zbl0821.17007

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.