3-LIE BIALGEBRAS
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...
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| Published in | Acta mathematica scientia Vol. 34; no. 2; pp. 513 - 522 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.03.2014
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0252-9602 1572-9087 |
| DOI | 10.1016/S0252-9602(14)60024-2 |
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| Abstract | 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. |
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| AbstractList | 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. 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. And the classification of 4-dimensional 3-Lie coalgebras and 3-dimensional 3-Lie bialgebras over an algebraically closed field of characteristic zero are provided. |
| Author | 白瑞蒲 程宇 李佳倩 孟伟 |
| AuthorAffiliation | College of Mathematics and Computer Science, Hebei University, Baoding 071002, China Department of Mathematics, Baoding University, Baoding 071002, China |
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| Cites_doi | 10.1007/BF00761714 10.1063/1.3436555 10.1088/1126-6708/2008/06/020 10.1088/1126-6708/2008/05/054 10.1007/s11464-011-0107-z 10.1016/0001-8708(80)90056-0 10.1081/AGB-120016755 10.1088/1751-8113/42/48/485206 10.1007/BF02009328 10.1007/BF01081585 10.1016/j.laa.2009.03.018 10.1016/j.nuclphysb.2008.11.014 10.1081/AGB-120017349 |
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| Copyright | 2014 Wuhan Institute of Physics and Mathematics Copyright © Wanfang Data Co. Ltd. All Rights Reserved. |
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| Keywords | 3-Lie coalgebra 3-Lie bialgebra 17D99 17B05 3-Lie algebra |
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| Notes | 3-Lie algebra; 3-Lie coalgebra; 3-Lie bialgebra 42-1227/O 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. Ruipu BAI, Yu CHENG, Jiaqian LIE（ College of Mathematics and Computer Science, Hebei University, Baoding 071002, China; Department of Mathematics, Baoding University, Baoding 071002, China; College of Mathematics and Computer Science, Hebei University, Baoding 071002, China; College of Mathematics and Computer Science, Hebei University, Baoding 071002, China） |
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| References | Ling (bib8) 1993 Bai, Shen, Zhang (bib12) 2009; 431 Filippov (bib1) 1985; 26 Bolavin, Drinfeld (bib16) 1982; 16 Kasymov (bib7) 1987; 26 Pozhidaev (bib10) 2003; 31 DeSmedt (bib17) 1994; 31 Ho, Hou, Matsuo (bib3) 2008; 0806 Gustavsson (bib5) 2009; B811 Jin, Liu, Zhang (bib11) 2009; 42 Pojidaev (bib9) 2003; 31 Bagger, Lambert (bib2) 2008; D77 Papadopoulos (bib6) 2008; 0805 Michaelis (bib15) 1980; 38 Bai, Song, Zhang (bib14) 2011; 6 Ho, Chebotar, Ke (bib4) 2003; 113 Bai, Bai, Wang (bib13) 2010; 51 Pozhidaev (10.1016/S0252-9602(14)60024-2_bib10) 2003; 31 Gustavsson (10.1016/S0252-9602(14)60024-2_bib5) 2009; B811 Jin (10.1016/S0252-9602(14)60024-2_bib11) 2009; 42 Kasymov (10.1016/S0252-9602(14)60024-2_bib7) 1987; 26 Bolavin (10.1016/S0252-9602(14)60024-2_bib16) 1982; 16 Papadopoulos (10.1016/S0252-9602(14)60024-2_bib6) 2008; 0805 Ho (10.1016/S0252-9602(14)60024-2_bib3) 2008; 0806 Michaelis (10.1016/S0252-9602(14)60024-2_bib15) 1980; 38 Pojidaev (10.1016/S0252-9602(14)60024-2_bib9) 2003; 31 Bai (10.1016/S0252-9602(14)60024-2_bib12) 2009; 431 Filippov (10.1016/S0252-9602(14)60024-2_bib1) 1985; 26 Ho (10.1016/S0252-9602(14)60024-2_bib4) 2003; 113 DeSmedt (10.1016/S0252-9602(14)60024-2_bib17) 1994; 31 Bagger (10.1016/S0252-9602(14)60024-2_bib2) 2008; D77 Ling (10.1016/S0252-9602(14)60024-2_bib8) 1993 Bai (10.1016/S0252-9602(14)60024-2_bib13) 2010; 51 Bai (10.1016/S0252-9602(14)60024-2_bib14) 2011; 6 |
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| Snippet | 3-Lie algebras have close relationships with many important fields in mathemat- ics and mathematical physics. This article concerns 3-Lie algebras. The... 3-Lie algebras have close relationships with many important fields in mathematics and mathematical physics. This article concerns 3-Lie algebras. The concepts... 3-Lie algebras have close relationships with many important fields in mathemat-ics and mathematical physics. This article concerns 3-Lie algebras. The concepts... |
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| SubjectTerms | 17B05 17D99 3-Lie algebra 3-Lie bialgebra 3-Lie coalgebra 代数和 代数闭域 数学物理 李代数 李双代数 |
| Title | 3-LIE BIALGEBRAS |
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