Results 51 to 60 of about 83 (77)
Trivial central extensions of Lie bialgebras
Journal of Algebra, 2013 23 ...
Marco Andrés Farinati
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Communications in Theoretical Physics, 2015
Abstract A compatible Lie algebra is a pair of Lie algebras such that any linear combination of the two Lie brackets is a Lie bracket. We construct a bialgebra theory of compatible Lie algebras as an analogue of a Lie bialgebra. They can also be regarded as a “compatible version” of Lie bialgebras, that is, a pair of Lie bialgebras such ...
Ming-Zhong Wu, Cheng-Ming Bai
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Abstract A compatible Lie algebra is a pair of Lie algebras such that any linear combination of the two Lie brackets is a Lie bracket. We construct a bialgebra theory of compatible Lie algebras as an analogue of a Lie bialgebra. They can also be regarded as a “compatible version” of Lie bialgebras, that is, a pair of Lie bialgebras such ...
Ming-Zhong Wu, Cheng-Ming Bai
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Jordan bialgebras and their relation to Lie bialgebras
Algebra and Logic, 1997We develop the notion of Jordan bialgebras and study the way in which such are related to Lie bialgebras. In particular, it is shown that if a Lie algebra L(J) obtained from a Jordan algebra J by applying the Kantor-Koecher-Tits construction admits the structure of a Lie bialgebra, under some natural constraints, then, J permits the structure of a ...
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On Quantization Functors of Lie Bialgebras
Acta Applicandae Mathematica, 2002This is a survey on recent work on quantization functors of Lie bialgebras. Let QUE be the category of quantized universal enveloping algebras over a field of characteristic 0, and let LBA be the category of Lie bialgebras. The operation of taking the semiclassical limit defines a functor \(\text{SC}:\text{QUE}\rightarrow \text{LBA}\).
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Communications in Algebra, 1998
We generalize Lie bialgebras and Lie bialgebioids to new objects which we call generalized Lie bialgebras. Similar to Lie bialgebras and Lie bial-gebroids, generalized Lie bialgebras are self-dual and generate canonically Hamiltonian structures on their representative spaces. We show that for a generalized Lie bialgebra (E, Ē), a pair (L 1,L 2) of E +Ē
Tan Youjun, Zhang-Ju Liu
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We generalize Lie bialgebras and Lie bialgebioids to new objects which we call generalized Lie bialgebras. Similar to Lie bialgebras and Lie bial-gebroids, generalized Lie bialgebras are self-dual and generate canonically Hamiltonian structures on their representative spaces. We show that for a generalized Lie bialgebra (E, Ē), a pair (L 1,L 2) of E +Ē
Tan Youjun, Zhang-Ju Liu
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Acta Mathematica Scientia, 2014
Abstract 3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied.
Ruipu BAI +3 more
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Abstract 3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The structures of such categories of algebras and the relationships with 3-Lie algebras are studied.
Ruipu BAI +3 more
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Lie Bialgebra Structures on the Lie Algebra
Communications in Algebra, 2013In the present article we shall investigate the Lie bialgebra structures on the Lie algebra , which are shown to be triangular coboundary.
Ying Xu, Junbo Li, Wei Wang
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Jordan bialgebras of symmetric elements and Lie bialgebras
Siberian Mathematical Journal, 1998In his previous article [|Algebra Logic 36, No. 1, 1-15 (1997); translation from Algebra Logika 36, No. 1, 3-25 (1997)], the author proved that if the Lie algebra \(L(J)\) built from a Jordan algebra \(J\) by the Kantor-Köcher-Tits construction admits the structure of a Lie bialgebra then, under certain natural restrictions, \(J\) admits the structure ...
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Quantizations of Lie bialgebras, duality involution and oriented graph complexes
Letters in Mathematical Physics, 2022Marko Živković
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