Results 31 to 40 of about 83 (77)
On the Classification of Lie Bialgebras by Cohomological Means
Documenta Mathematica, 2019 We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint of descent and non-abelian cohomology. We achieve a description of the problem in terms of faithfully flat cohomology over an arbitrary ring over \mathbb{Q}
Alsaody, Seidon, Pianzola, Arturo
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Lie bialgebras constructed from Zinbiel bialgebras and Leibniz bialgebras
There is a Lie algebra structure on the tensor product of a Leibniz algebra and a Zinbiel algebra for the operads of Leibniz algebras and Zinbiel algebras are Koszul dual. In this paper, we extend such conclusion to the context of bialgebras. We show that there is a Lie bialgebra structure on the tensor product of a Leibniz bialgebra and a quadratic ...
Hou, Bo, Lin, Yuanchang
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, 2012 3-Lie algebra; 3-Lie coalgebra; 3-Lie ...
Bai, Ruipu, Li, Jiaqian, Meng, Wei
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In this paper, we establish a bialgebra theory for Reynolds Lie algebras. First we introduce the notion of a quadratic Reynolds Lie algebra and show that it induces an isomorphism from the adjoint representation to the coadjoint representation. Then we introduce the notion of matched pairs, Manin triples and bialgebras for Reynolds Lie algebras, and ...
Hou, Shuai, Goncharov, Maxim
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Nijenhuis pre-Lie bialgebras, Nijenhuis Lie bialgebras and \sss-equation
Two aspects on the important notion of pre-Lie algebras are pre-Lie bialgebras (or left-symmetric bialgebras) with motivation from para-Kähler Lie algebras, and Nijenhuis operators on pre-Lie algebras arising from their deformation theory. In this paper, we present a method to construct Nijenhuis operators on a pre-Lie algebras via pseudo-Hessian pre ...
Guo, Li, Ma, Tianshui
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Infinitesimal Hom-bialgebras and Hom-Lie bialgebras
, 2010 We study the Hom-type generalization of infinitesimal bialgebras, called infinitesimal Hom-bialgebras. In particular, we consider infinitesimal Hom-bialgebras arising from quivers, the sub-classes of coboundary and quasi-triangular infinitesimal Hom-bialgebras, the associative Hom-Yang-Baxter equation, and homological perturbation of the ...
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Combinatorial Lie bialgebras of curves on surfaces
Topology, 2004 28 pages, 7 ...
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Bialgebra cohomology, deformations, and quantum groups. [PDF]
Proc Natl Acad Sci U S A, 1990 Gerstenhaber M, Schack SD.
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Shifted Poisson structures on higher Chevalley-Eilenberg algebras. [PDF]
Lett Math PhysKemp C, Laugwitz R, Schenkel A.
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