Enhancing Lie color algebras

Abstract

Lie color algebras generalize Lie superalgebras. We adapt a construction of Bahturin and Pagon to create enhanced Lie color algebras. This construction offers a much-needed method for constructing simple Lie color algebras. To illustrate its applicability, we demonstrate how to enhance any simple Lie superalgebra and obtain a simple Lie color algebra. Additionally, we show that if a Lie color algebra has a nonzero determinant, this property extends to its enhancement. This ensures its universal enveloping algebra is semiprime. Extra conditions on the grading group provide a primeness criterion.

KEYWORDS:

• Lie color algebra
• universal enveloping algebra

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 17B75
• 17B35

Acknowledgments

The author would like to thank the referee for conducting a rigorous evaluation and offering useful feedback which improved this publication.