Yidong Jin et al 2009 J. Phys. A: Math. Theor. 42 485206 doi:10.1088/1751-8113/42/48/485206
Real simple n-Lie algebras admitting metric structures*
Yidong Jin1, Wenli Liu2,3 and Zhixue Zhang2
Show affiliationsWe give the multiplication structures of all real simple n-Lie algebras and prove that each of them has metric dimension 1 or 2 depending on that it belongs to type I or type II. We also determine the signatures of metrics on all real simple n-Lie algebras. Moreover, we present an example of real 3-Lie algebras which is indecomposable but has much larger metric dimension.
- Footnote
- PACS
- MSC
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81T60 Supersymmetric field theories
81T30 String and superstring theories; other extended objects (e.g., branes) (See also 83E30)
17Bxx Lie algebras and Lie superalgebras (For Lie groups, see 22Exx)
81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)
- Subjects
- Dates
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Issue 48 (4 December 2009)
Received 3 May 2009, in final form 16 October 2009
Published 13 November 2009
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Real simple n-Lie algebras admitting metric structures
Yidong Jin et al 2009 J. Phys. A: Math. Theor. 42 485206
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