Poisson and Filippov superalgebras

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• 作者：A. P. Pozhidaev
• 关键词：Poisson superalgebra ; Filippov superalgebra ; simple superalgebra ; Grassmann superalgebra
• 刊名：Siberian Mathematical Journal
• 出版年：2015
• 出版时间：May 2015
• 年：2015
• 卷：56
• 期：3
• 页码：505-515
• 全文大小：192 KB
• 参考文献：1. Farkas D. R., 鈥淧oisson polynomial identities,鈥?Comm. Algebra, 26, No. 2, 401鈥?16 (1998).MATH MathSciNet View Article
  2. Kantor I. L., 鈥淛ordan and Lie superalgebras determined by a Poisson algebra,鈥?in: Proceedings of the Second Siberian School 鈥淎lgebra and Analysis鈥?(Tomsk, 1989), Amer. Math. Soc., Providence, 1992, pp. 55鈥?0.
  3. Bai R. and Wu Y., 鈥淐onstructing 3-Lie algebras,鈥?http://鈥媋rxiv.鈥媜rg/鈥媝df/鈥?306.鈥?994.鈥媝df .
  4. Pojidaev A. P., 鈥淪imple n-Lie algebras,鈥?Algebra and Logic, 38, No. 3, 181鈥?92 (1999).MathSciNet View Article
  5. Pojidaev A. P., 鈥淓nveloping algebras of Filippov algebras,鈥?Comm. Algebra, 31, No. 2, 883鈥?00 (2003).MATH MathSciNet View Article
  6. Cantarini N. and Kac V. G., 鈥淐lassification of simple linearly compact n-Lie superalgebras,鈥?Comm. Math. Phys., 298, 833鈥?53 (2010).MATH MathSciNet View Article
  7. Bremner M., 鈥淰arieties of anticommutative n-ary algebras,鈥?J. Algebra, 191, No. 1, 76鈥?8 (1997).MATH MathSciNet View Article
  
• 作者单位：A. P. Pozhidaev (1)
  
  1. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Russian Library of Science
  
• 出版者：Springer New York
• ISSN：1573-9260

文摘

We establish a connection between the Poisson superalgebras with some additional (Farkas) identity and the Filippov superalgebras. This construction yields all available simple Filippov algebras. We also exhibit new examples of simple finite-dimensional Filippov superalgebras of characteristic 2.