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Rational forms for twistings of enveloping algebras of simple Lie algebras

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Abstract

We give ‘rational’ forms for twistings of classical enveloping algebras. We also remark a link with the ‘generalized formalism’ of Gurevich, Manin, and Cartier.

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References

  1. Andruskiewitsch, N. and Enriquez, B., Examples of compact matrix pseudogroups arising from the twisting operation, to appear in Comm. Math. Phys.

  2. BelavinA. A. and Drinfel'dV. G., On the solutions of the classical Yang-Baxter equations for simple Lie algebras, Funkt. Anal. i Prilozhen. 3, 1–29 (1982).

    Google Scholar 

  3. Drinfel'dV. G., Quasi-Hopf algebras, Leningrad Math. J. 1, 1419–1457 (1990).

    Google Scholar 

  4. Drinfel'dV. G., On constant, quasi-classical solutions of the Yang-Baxter equation, Soviet Math. Dokl. 28(3), 667–673 (1983).

    Google Scholar 

  5. Gurevich, D., Radul, A., and Rubtsov, V., Non-commutative differential geometry and the Yang-Baxter equation, preprint.

  6. LevendorskiiS., Twisted algebra of functions on compact quantum groups, and their representations (in Russian), Algebra i Analiz 3, 180–198 (1991).

    Google Scholar 

  7. LevendorskiiS. and SoibelmanYa. S., Algebra of functions on the compact quantum groups, Schubert cells and quantum Tori, Comm. Math. Phys. 139, 141–170 (1991).

    Google Scholar 

  8. Manin, Yu., Quantum groups and non-commutative geometry, Montréal.

  9. Okado, M. and Yamane, H., R-matrices with gauge parameters and multiparameter quantized enveloping algebras, preprint.

  10. ReshetikhinN., Multiparameter quantum groups and twisted quasitriangular Hopf algebras, Lett. Math. Phys. 20, 331–335 (1990).

    Google Scholar 

  11. Soibelman, Ya. S., Irreducible representations of the function algebra on the quantum SU(n) and Schubert cells, Soviet Math. Dokl. 40(1) (1990).

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Enriquez, B. Rational forms for twistings of enveloping algebras of simple Lie algebras. Lett Math Phys 25, 111–120 (1992). https://doi.org/10.1007/BF00398307

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  • DOI: https://doi.org/10.1007/BF00398307

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