Classifications of (n + k)-dimensional metric n-Lie algebras
We study the structure of isotropic ideals of the metric n-Lie algebra over the complex field for n 2. Based on the study of isotropic ideals of metric n-Lie algebras in this paper, we obtain the following. (i) Let be the Levi decomposition and without semi-simple ideals. If n > 2, is perfect and...
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| Veröffentlicht in: | Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2013-04, Vol.46 (14), p.145202-11 |
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| creator | Bai, Ruipu Wu, Wanqing Chen, Zhiqi |
| description | We study the structure of isotropic ideals of the metric n-Lie algebra over the complex field for n 2. Based on the study of isotropic ideals of metric n-Lie algebras in this paper, we obtain the following. (i) Let be the Levi decomposition and without semi-simple ideals. If n > 2, is perfect and is isotropic, then is the unique isomaximal ideal and , and the metric dimension of is m. If is indecomposable, then is isomorphic to as an -module in the regular representation. (ii) If with 2 k n + 1, then . If is unsolvable, then is reductive. If the center of is isotropic, then (iii) There are only three classes of (n + k)-dimensional metric n-Lie algebras for 2 k n + 1 and n > 2, and the concrete multiplications for each class are provided. |
| doi_str_mv | 10.1088/1751-8113/46/14/145202 |
| format | Article |
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Based on the study of isotropic ideals of metric n-Lie algebras in this paper, we obtain the following. (i) Let be the Levi decomposition and without semi-simple ideals. If n > 2, is perfect and is isotropic, then is the unique isomaximal ideal and , and the metric dimension of is m. If is indecomposable, then is isomorphic to as an -module in the regular representation. (ii) If with 2 k n + 1, then . If is unsolvable, then is reductive. 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If the center of is isotropic, then (iii) There are only three classes of (n + k)-dimensional metric n-Lie algebras for 2 k n + 1 and n > 2, and the concrete multiplications for each class are provided.</description><subject>Algebra</subject><subject>classification</subject><subject>Classifications</subject><subject>Concretes</subject><subject>Decomposition</subject><subject>isomaximal ideal</subject><subject>isotropic ideal</subject><subject>Lie algebra</subject><subject>Mathematical analysis</subject><subject>metric</subject><subject>Multiplication</subject><subject>Representations</subject><issn>1751-8113</issn><issn>1751-8121</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2013</creationdate><recordtype>article</recordtype><recordid>eNqFkFtLxDAQhYMouK7-BenjitRmmksT8EUWb7Dgiz6HNJ1I1l7WpPvgv7dLF1-FgRlmzjkwHyHXQO-AKlVAJSBXAKzgsgA-lShpeUIWx0MJp38zsHNykdKWUsGpLhfkft3alIIPzo5h6FM2-GzVZ7fZ103ehA77NG1tm3U4xuCyPt8EzGz7iXW06ZKcedsmvDr2Jfl4enxfv-Sbt-fX9cMmd2WlxhycdKi9VlizSnDdgGC1Egot806hqKTW3laaeqgbxMp6R5VztWt8YyVnbElWc-4uDt97TKPpQnLYtrbHYZ8MyCkBGFA-SeUsdXFIKaI3uxg6G38MUHPAZQ4kzIGE4dIANzOuyVjOxjDszHbYx-nr9J_pF7ETa7A</recordid><startdate>20130412</startdate><enddate>20130412</enddate><creator>Bai, Ruipu</creator><creator>Wu, Wanqing</creator><creator>Chen, Zhiqi</creator><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20130412</creationdate><title>Classifications of (n + k)-dimensional metric n-Lie algebras</title><author>Bai, Ruipu ; Wu, Wanqing ; Chen, Zhiqi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c278t-1c6ce9f98eb37549d153b858ea3fc8e57699fa790f1bdee7afc08ccbcdfda6433</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2013</creationdate><topic>Algebra</topic><topic>classification</topic><topic>Classifications</topic><topic>Concretes</topic><topic>Decomposition</topic><topic>isomaximal ideal</topic><topic>isotropic ideal</topic><topic>Lie algebra</topic><topic>Mathematical analysis</topic><topic>metric</topic><topic>Multiplication</topic><topic>Representations</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bai, Ruipu</creatorcontrib><creatorcontrib>Wu, Wanqing</creatorcontrib><creatorcontrib>Chen, Zhiqi</creatorcontrib><collection>CrossRef</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of physics. 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| subjects | Algebra classification Classifications Concretes Decomposition isomaximal ideal isotropic ideal Lie algebra Mathematical analysis metric Multiplication Representations |
| title | Classifications of (n + k)-dimensional metric n-Lie algebras |
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