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

DOI10.1063/1.532471zbMATH Open0928.17009arXivq-alg/9706016OpenAlexW3104623756MaRDI QIDQ4701622

César Bautista

Publication date: 21 November 1999

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Abstract: A proof of Poincar'e-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 Poincar'e-Birkhoff-Witt theorem and we show that they are genuine universal enveloping algebras of certain generalized Lie algebras.

Full work available at URL: https://arxiv.org/abs/q-alg/9706016

zbMATH Keywords

quantized universal enveloping algebrasPoincaré-Birkhoff-Witt theoremnonstandard quantum deformation\(S\)-Lie algebras\(T\)-Lie algebras

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Universal enveloping (super)algebras (17B35) Color Lie (super)algebras (17B75) Ring-theoretic aspects of quantum groups (16T20)

Related Items (3)

On the generalized enveloping algebra of a color Lie algebra ⋮ A Poincar\'e-Birkhoff-Witt Theorem for profinite pronilpotent Lie algebras ⋮ Poisson color algebras of arbitrary degree

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