In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-...In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.展开更多
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
We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±,...We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.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
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
基金The NSF(11047030 and 11771122) of Chinathe Science and Technology Program(152300410061) of Henan Province
文摘In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.
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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175113 and 11275123)the Key Project of Natural Science Fund of Anhui Province,China(Grant No.KJ2013A261)
文摘We consider the quantum mechanical SU（2） transformation e^2λJzJ±e^-2λJz = e^±2λJ±as if the meaning of squeezing with e^±2λ being squeezing parameter. By studying SU（2） operators （J±, Jz） from the point of view of squeezing we find that （J±,Jz） can also be realized in terms of 3-mode bosonic operators. Employing this realization, we find the natural representation （the eigenvectors of J＋ or J-） of the 3-mode squeezing operator e^2λJz. The idea of considering quantum SU（2） transformation as if squeezing is liable for us to obtain the new bosonic operator realization of SU（2） and new squeezing operators.
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.
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.
