## Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras, Published as Chapter 17, pp 189-206 (2008)

Venue: | Generalized Lie theory in Mathematics, Physics and Beyond |

Citations: | 15 - 4 self |

### BibTeX

@INPROCEEDINGS{Makhlouf08hom-lieadmissible,

author = {A. Makhlouf and S. Silvestrov},

title = {Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras, Published as Chapter 17, pp 189-206},

booktitle = {Generalized Lie theory in Mathematics, Physics and Beyond},

year = {2008},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

Abstract. The aim of this paper is to generalize the concept of Lie-admissible coalgebra introduced in [2] to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures introduced in [12].

### Citations

294 | algebras and their actions on rings - Montgomery, Hopf |

261 | algebras and the quantum Yang–Baxter equation - Drinfel’d, Hopf - 1985 |

107 | Foundations of Quantum Group Theory,” Cambridge Univ - Majid |

35 |
Deformations of Lie algebras using σ-derivations
- Hartwig, Larsson, et al.
(Show Context)
Citation Context ...ble coalgebra introduced in [2] to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures introduced in [12]. Introduction In =-=[4, 7, 8]-=-, the class of quasi-Lie algebras and subclasses of quasi-hom-Lie algebras and Hom-Lie algebras has been introduced. These classes of algebras are tailored in a way suitable for simultaneous treatment... |

22 |
Quasi-hom-Lie Algebras, Central Extensions and 2-cocycle-like Identities
- Larsson, Silvestrov
(Show Context)
Citation Context ...ble coalgebra introduced in [2] to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures introduced in [12]. Introduction In =-=[4, 7, 8]-=-, the class of quasi-Lie algebras and subclasses of quasi-hom-Lie algebras and Hom-Lie algebras has been introduced. These classes of algebras are tailored in a way suitable for simultaneous treatment... |

12 |
Quasi-Lie algebras, in ”Non-commutative geometry and representation theory in mathematical physics
- Larsson, Silvestrov
- 2004
(Show Context)
Citation Context ...ble coalgebra introduced in [2] to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures introduced in [12]. Introduction In =-=[4, 7, 8]-=-, the class of quasi-Lie algebras and subclasses of quasi-hom-Lie algebras and Hom-Lie algebras has been introduced. These classes of algebras are tailored in a way suitable for simultaneous treatment... |

12 |
Quasi-deformations of sl2(F) using twisted derivations
- Larsson, Silvestrov
(Show Context)
Citation Context ...ng in connection with twisted, discretized or deformed derivatives and corresponding generalizations, discretizations and deformations of vector fields and differential calculus. It has been shown in =-=[4, 7, 8, 9]-=- that the class of quasi-Hom-Lie algebras contains as a subclass on the one hand the color Lie algebras and in particular Lie superalgebras and Lie algebras, and on the another hand various known and ... |

11 | Silvestrov: Commuting elements in q-deformed Heisenberg algebras - Hellström, D |

7 |
Lie admissible coalgebras
- Remm
(Show Context)
Citation Context ...BRAS AND HOM-HOPF ALGEBRAS A. MAKHLOUF AND S. SILVESTROV arXiv:0709.2413v1 [math.RA] 15 Sep 2007 Abstract. The aim of this paper is to generalize the concept of Lie-admissible coalgebra introduced in =-=[2]-=- to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures introduced in [12]. Introduction In [4, 7, 8], the class of quasi-L... |

4 | rigidity and irreducible components of Hopf algebras - Makhlouf, Degeneration |

1 | groupes quantiques - Guichardet - 1995 |

1 | Quantum groups Spriner-Verlag, Graduate Text - Kassel - 1995 |

1 |
Hom-algebra structures, to appear in J. Gen. Lie Theory Appl
- Makhlouf, Silvestrov
(Show Context)
Citation Context ...concept of Lie-admissible coalgebra introduced in [2] to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures introduced in =-=[12]-=-. Introduction In [4, 7, 8], the class of quasi-Lie algebras and subclasses of quasi-hom-Lie algebras and Hom-Lie algebras has been introduced. These classes of algebras are tailored in a way suitable... |

1 |
Enveloping algebra of Hom-Lie algebras, to appear in J. Gen. Lie Theory Appl. Abdenacer Makhlouf, Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Application, 4, rue des Frères Lumière F-68093
- Yau
(Show Context)
Citation Context ...ons and properties of the enveloping algebras of Hom-Lie algebras are yet to be properly studied in full generality. An important progress in this direction has been made in the recent work by D. Yau =-=[14]-=-. In the present paper we develop the coalgebra counterpart of the notions and results of [12], extending in particular in the framework of Hom-associative and Hom-Lie algebras and Hom-coalgebras, the... |