A Poincaré-birkhoff-witt Theorem for Generalized Lie Color Algebras
نویسنده
چکیده
A proof of Poincaré-Birkhoff-Witt theorem is given for a class of generalized Lie algebras closely related to the Gurevich S-Lie algebras. As concrete examples, we construct the positive (negative) parts of the quantized universal enveloping algebras of type An and Mp,q,ǫ(n, K), which is a nonstandard quantum deformation of GL(n). In particular, we get, for both algebras, a unified proof of the Poincaré-Birkhoff-Witt theorem and we show that they are genuine universal enveloping algebras of certain generalized Lie algebras. PACS numbers: 02.10.Vr, 02.10.Tq, 02.20.Sv Running title: PBW for generalized Lie color algebras
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Differential Calculi of Poincaré-Birkhoff-Witt type on Universal Enveloping Algebras
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