3-Lie algebras have close relationships with many important fields in mathemat- ics and mathematical physics. This article concerns 3-Lie algebras. The concepts of 3-Lie coalgebras and 3-Lie bialgebras are given. The ...3-Lie algebras have close relationships with many important fields in mathemat- ics 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. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char- acteristic zero are provided.展开更多
In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and ...In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras.展开更多
In this paper, based on the existing research results, we obtain the unary extension 3-Lie algebras by one-dimensional extension of the known Lie algebra L. For two known 3-Lie algebras <em>H</em>, <em&...In this paper, based on the existing research results, we obtain the unary extension 3-Lie algebras by one-dimensional extension of the known Lie algebra L. For two known 3-Lie algebras <em>H</em>, <em>M</em>, the (<i>μ</i>, <i>ρ</i>, <i>β</i>)-extension of <em>H</em> through <em>M</em> is given, and the necessary and sufficient conditions for the (<i>μ</i>, <i>ρ</i>, <i>β</i>)-extension algebra of <em>H</em> through <em>M</em> being 3-Lie algebra are obtained, and the structural characteristics and properties of these two kinds of extended 3-Lie algebras are given.展开更多
基金partially supported by NSF(11371245)of ChinaNSF(A2010000194)of Hebei Province
文摘3-Lie algebras have close relationships with many important fields in mathemat- ics 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. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of char- acteristic zero are provided.
文摘In this paper, we mainly investigate the realization of 3-Lie algebras from a family of Lie algebras. We prove the realization theorem, offer a concrete example realizing all type of 4-dimensional 3-Lie algebras, and also give some properties about semi-simple n-Lie algebras.
文摘In this paper, based on the existing research results, we obtain the unary extension 3-Lie algebras by one-dimensional extension of the known Lie algebra L. For two known 3-Lie algebras <em>H</em>, <em>M</em>, the (<i>μ</i>, <i>ρ</i>, <i>β</i>)-extension of <em>H</em> through <em>M</em> is given, and the necessary and sufficient conditions for the (<i>μ</i>, <i>ρ</i>, <i>β</i>)-extension algebra of <em>H</em> through <em>M</em> being 3-Lie algebra are obtained, and the structural characteristics and properties of these two kinds of extended 3-Lie algebras are given.
