Results 11 to 20 of about 246,696 (68)
A triple construction for Lie bialgebras [PDF]
, 2005 We study the triple of a quasitriangular Lie bialgebra as a natural extension of the Drinfel’d double. The triple is itself a quasitriangular Lie bialgebra.
Grabowski, Jan
core +3 more sources
On Lie induction and the exceptional series [PDF]
, 2005 Lie bialgebras occur as the principal objects in the infinitesimalization of the theory of quantum groups — the semi-classical theory. Their relationship with the quantum theory has made available some new tools that we can apply to classical questions ...
GRABOWSKI, JANE, Grabowski, Jan
core +3 more sources
Elementary Lie Algebras and Lie A-Algebras. [PDF]
, 2007 A finite-dimensional Lie algebra L over a field F is called elementary if each of its subalgebras has trivial Frattini ideal; it is an A-algebra if every nilpotent subalgebra is abelian. The present paper is primarily concerned with the classification of
Varea, Vicente R., Towers, David A.
core +3 more sources
Braided Lie bialgebras associated to Kac-Moody algebras [PDF]
, 2008 Braided-Lie bialgebras have been introduced by Majid, as the Lie versions of Hopf algebras in braided categories. In this paper we extend previous work of Majid and of ours to show that there is a braided-Lie bialgebra associated to each inclusion of Kac-
Grabowski, Jan
core +2 more sources
Inductive constructions for Lie bialgebras and Hopf algebras [PDF]
, 2006 In recent years, two generalisations of the theory of Lie algebras have become prominent, namely the "semi-classical" theory of Lie bialgebras and the "quantum" theory of Hopf algebras, including the quantized enveloping algebras.
Majid, Shahn +3 more
core +1 more source
The theorem of Lie and hyperplane subalgebras of Lie algebras [PDF]
, 1992 Poguntke D. The theorem of Lie and hyperplane subalgebras of Lie algebras. Geometriae Dedicata.
Poguntke, Detlev
core +1 more source
Hom‐Yang‐Baxter Equations and Frobenius Monoidal Hom‐Algebras
Advances in Mathematical Physics, Volume 2018, Issue 1, 2018., 2018 It is shown that quasi‐Frobenius Hom‐Lie algebras are connected with a class of solutions of the classical Hom‐Yang‐Baxter equations. Moreover, a similar relation is discussed on Frobenius (symmetric) monoidal Hom‐algebras and solutions of quantum Hom‐Yang‐Baxter equations. Monoidal Hom‐Hopf algebras with Frobenius structures are studied at last.
Yuanyuan Chen +2 more
wiley +1 more source
The Factorization for a Class of Hom‐Coalgebras
Advances in Mathematical Physics, Volume 2017, Issue 1, 2017., 2017 Let (H, α) be a Hom‐Hopf algebra and (C, β) a Hom‐coalgebra. In this paper, we first introduce the notions of Hom‐crossed coproduct C ⋊λ H and cleft coextension and then discuss the equivalence between them. Furthermore, we discuss the relation between cleft coextension and Hom‐module coalgebra with the Hom‐Hopf module structure and obtain a Hom ...
Lihong Dong +3 more
wiley +1 more source
Hom‐O‐Operators and Hom‐Yang‐Baxter Equations
Advances in Mathematical Physics, Volume 2015, Issue 1, 2015., 2015 In Hom‐Lie set, we introduce the concept of Hom‐O‐operators and study its relation with classical Hom‐Yang‐Baxter equation, as well as left‐symmetric Hom‐algebras. We construct the corresponding relation between left‐symmetric Hom‐algebras and Hom‐1‐cocycles, which are both related to classical Hom‐Yang‐Baxter equation. Moreover, in Hom‐algebra setting,
Yuanyuan Chen +2 more
wiley +1 more source
Two Generator Subalgebras Of Lie Algebras. [PDF]
, 2007 In [14] Thompson showed that a finite group G is solvable if and only if every twogenerated subgroup is solvable (Corollary 2, p. 388). Recently, Grunevald et al.
Kevin Bowman +5 more
core +3 more sources