Enveloping algebras of Hom-Lie algebras

By Donald Yau. 2007

137 citations recorded by the source corpus.

Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed. 2000 MSC: 05C05, 17A30, 17A32, 17A50, 17B01, 17B35, 17D25 1

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/017883c0d645706f30a64d73d4de5d95ca1f1689

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Florin Panaite
2. Abdenacer Makhlouf
3. Donald Yau
4. Y. Sheng
5. G. Graziani
6. Claudia Menini
7. Stefaan Caenepeel
8. I. Goyvaerts

In Discrete Mathematics and Combinatorics

1. Abdenacer Makhlouf
2. J. Teles
3. C. Laurent-Gengoux
4. Y. Sheng
5. I. Goyvaerts
6. Stefaan Caenepeel
7. Florin Panaite
8. José Manuel Casas

In Geometry and Topology

1. Abdenacer Makhlouf
2. Florin Panaite
3. Donald Yau
4. Y. Sheng
5. G. Graziani
6. Claudia Menini
7. Stefaan Caenepeel
8. I. Goyvaerts

Citations in the corpus

• On universal central extensions of Hom-Lie algebras (2012, background): “The study of this algebraic structure was the subject of several papers [4, 7, 8, 9, 11].”
• BiHom-associative algebras, BiHom-Lie algebras and BiHom-bialgebras (2015, background): “Enveloping algebras of Hom-Lie algebras where introduced in [29] (see also [8, Section 8]).”
• Hom-bialgebras and comodule Hom-algebras (2008, methodology): “there is an enveloping Hom-associative algebra functor UHLie going the other way, from Hom-Lie algebras to Hom-associative algebras [24].”
• Hom-algebras and homology (2007, background): “Besides [21, 26, 27, 30, 31], Hom-algebras have been further studied in [2, 5, 8, 10, 11, 12, 17, 22, 23, 24, 29, 32, 33, 34].”
• Universal Algebra of a Hom-Lie Algebra and group-like elements (2015, methodology): “sociative algebras, called Hom-associative algebras, were introduced in [MS1], where it is shown that they are Hom-Lie admissible, while the enveloping algebra of a Hom-Lie algebra was constructed in [Yau1]. Moreover, Hombialgebras and Hom-Hopf algebras were studied in [MS2, MS5, Yau4]. Further resu”
• The Hom–Yang–Baxter equation, Hom–Lie algebras, and quasi-triangular bialgebras (2009, background): “Although it is not needed in this paper, we point out that, similar to the universal enveloping algebra of a Lie algebra, there is a universal enveloping Hom-associative algebra functor U from Hom–Lie algebras to Hom-associative algebras [26, 28].”
• Monoidal Hom–Hopf Algebras (2009, background): “One would expect that this is a Hom–Hopf algebra, but such a result does not appear in [12].”
• Representations of Hom-Lie Algebras (2010, background): “Because of close relation to discrete and deformed vector fields and differential calculus [5, 7, 8], hom-Lie algebras are widely studied recently [1, 2, 9, 10, 12, 13, 14].”