✨
AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, the construction is applied to obtain the well-known Poincaré-Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.
📌 3 Key Takeaways
🎯
Objective & Hypothesis:In this paper, the universal enveloping algebra of color hom-Lie algebras is studied.
📊
Key Findings & Data:A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to obtain the universal enveloping algebra of an involutive hom-Lie color algebra.
💡
Conclusion & Impact:Finally, the construction is applied to obtain the well-known Poincaré-Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Color hom-Lie algebra · enveloping algebra
Abstract
In this paper, the universal enveloping algebra of color hom-Lie algebras is studied. A construction of the free involutive hom-associative color algebra on a hom-module is described and applied to obtain the universal enveloping algebra of an involutive hom-Lie color algebra. Finally, the construction is applied to obtain the well-known Poincaré-Birkhoff-Witt theorem for Lie algebras to the enveloping algebra of an involutive color hom-Lie algebra.
🔖
Cite This Article
ARMAKAN, A., SILVESTROV, S., FARHANGDOOST, M. R. (2019). Enveloping algebras of color hom-Lie algebras. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 1, 316–339. https://ajindex.com/articles/215006