Braided modules and reflection equations

Dimitri Gurevich

Banach Center Publications (1997)

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

Abstract

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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.

How to cite

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Gurevich, 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

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  3. [DG1] J. Donin, D. Gurevich, Braiding of the Lie algebra s l ( 2 ) , Amer. Math. Soc. Transl. (2) 167 (1995), pp. 23-36. Zbl0853.17009
  4. [DG2] J. Donin, D. Gurevich, Quantum orbits of R-matrix type, Lett. Math. Phys. 35 (1995), pp. 263-276. Zbl0853.17010
  5. [DGR] J. Donin, D. Gurevich, V. Rubtsov, Quantum hyperboloid and braided modules, q-alg/9511014. 
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  8. [GR] D. Gurevich, V. Rubtsov, Quantization of Poisson pencils and generalized Lie algebras, Teor. i Mat. Phys. 103 (1995), pp. 476-488. Zbl0855.58032
  9. [I1] A. Isaev, Interrelation between Quantum Groups and Reflection Equation (Braided) Algebras, Lett. Math. Phys. 34 (1995), pp. 333-341. Zbl0878.17012
  10. [I2] A. Isaev, Quantum Groups and Yang-Baxter Equation, Phys. Part. Nucl. 26 (1995) n 5, pp. 501-526 (Russian). 
  11. [IP1] A. Isaev, P. Pyatov, G L q ( N ) -covariant quantum algebras and covariant differential calculus, Phys. Let. A 179 (1993), pp.81-90. 
  12. [IP2] A. Isaev, P. Pyatov, Covariant differential complex on quantum linear groups, J. Phys. A: Math. Gen. 28 (1995), pp. 2227-2246. Zbl0860.58003
  13. [KSS] P. Kulish, R. Sasaki, C. Schwiebert, Constant Solution of Reflection Equations and Quantum Groups, hep-th/9205039. Zbl0799.17010
  14. [LS] V. Lyubashenko, A. Sudbery, Quantum Lie algebras of type A n , q-alg/9510004. 
  15. [M] Sh. Majid, Quantum and braided Lie algebras, JGP 13 (1994), pp.307-356. Zbl0821.17007

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