A Poincaré-Birkhoff-Witt theorem for generalized color Lie algebras

Cesar Bautista

doi:10.1063/1.532471

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A Poincaré-Birkhoff-Witt theorem for generalized color Lie algebras

Cesar Bautista

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Abstract

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 A_n and M_{p,q,e}(n,K), which is a non-standard 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.

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BibTeX RIS

Cesar Bautista. 1998-01-28. A Poincaré-Birkhoff-Witt theorem for generalized color Lie algebras. https://doi.org/10.1063/1.532471

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