Gröbner-Shirshov bases for quantum enveloping algebras
We give a method for finding Gröbner-Shirshov bases for the quantum enveloping algebras of Drinfel’d and Jimbo, show how the methods can be applied to Kac-Moody algebras, and explicitly find the bases for quantum enveloping algebras of typeAN(forq8≠1).
- [AL]W. Adams and P. Loustaunou,An Introduction to Gröbner Bases, Graduate Studies in Mathematics Vol. 3, American Mathematical Society, 1994. MR 95g:13025.Google Scholar
- [BoKl1]L. A. Bokut’ and A. A. Klein,Serre relations and Gröbner-Shirshov bases for simple Lie algebras I, International Journal of Algebra and Computation, to appear.Google Scholar
- [BoKl2]L. A. Bokut’ and A. A. Klein,Serre relations and Gröbner-Shirshov bases for simple Lie algebras II, International Journal of Algebra and Computation, to appear.Google Scholar
- [BoKu]L. A. Bokut’ and G. P. Kukin,Algorithmic and Combinatorial Algebras, Kluwer, Amsterdam, 1994. MR95i:17002.Google Scholar
- [BW]T. Becker and V. Weispfenning,Gröbner Bases. A Computational Approach to Commutative Algebra, Graduate Texts in Mathematics Vol. 141, Springer-Verlag, Berlin, 1993. MR 95e:13018.Google Scholar
- [Sh1]A. I. Shirshov,On free Lie rings, Matematicheskii Sbornik45 (1958), no. 2, 113–122.Google Scholar