On the Cohomology and Extensions of First-Class n-Lie Superalgebras

REFERENCES

• Azcárraga , J. A. , Izquierdo , J. M. ( 2010 ). n-ary algebras: a review with applications . J. Phys. A: Math. Theory. 44 : 293001, p. 117 .
   Google Scholar
• Bagger , J. , Lambert , N. ( 2008 ). Gauge symmetry and supersymmetry of multiple M2-branes . Phys. Rev. D 77 ( 6 ): 065008, 6 pp .
   Web of Science ®Google Scholar
• Bagger , J. , Lambert , N. ( 2008 ). Comments on multiple M2-branes . J. High Energy Phys. ( 2 ): 105 .
   Google Scholar
• Bajo , I. , Benayadi , S. , Medina , A. ( 2007 ). Symplectic structures on quadratic Lie algebras . J. Algebra 316 ( 1 ): 174 – 188 .
   Web of Science ®Google Scholar
• Bahturin , Y. A. , Mikhalev , A. A. , Petrogradsky , V. M. , Zaicev , M. V. ( 1992 ). Infinite-dimensional Lie superalgebras . de Gruyter Expositions in Mathematics . Vol. 7 . Berlin : Walter de Gruyter & Co .
   Google Scholar
• Bai , R. P. , Li , Y. ( 2011 ). -extensions of n-Lie algebras . ISRN Algebra 11 .
   Google Scholar
• Bordemann , M. ( 1997 ). Nondegenerate invariant bilinear forms on nonassociative algebras . Acta Math. Univ. Comenianae LXVI ( 2 ): 151 – 201 .
   Google Scholar
• Cantarini , N. , Kac , V. G. ( 2010 ). Classification of simple linearly compact n-Lie superalgebras . Comm. Math. Phys. 298 ( 3 ): 833 – 853 .
   Web of Science ®Google Scholar
• Chevalley , C. , Eilenberg , S. ( 1948 ). Cohomology theory of Lie groups and Lie algebras . Trans. Amer. Math. Soc. 63 : 85 – 124 .
   Web of Science ®Google Scholar
• Filippov , V. T. ( 1985 ). n-Lie algebras . (Russian) Sibirsk. Mat. Zh. 26 ( 6 ): 126 – 140 , 191 .
   Web of Science ®Google Scholar
• Gustavsson , A. ( 2009 ). Algebraic structures on parallel M2 branes . Nuclear Phys. B 811 ( 1–2 ): 66 – 76 .
   Web of Science ®Google Scholar
• Karpilovsky , G. ( 1990 ). Symmetric and G-algebras . With applications to group representations. Mathematics and its Applications . Vol. 60 . Dordrecht : Kluwer Academic Publishers Group .
   Google Scholar
• Kasymov , Sh. M. ( 1987 ). On a theory of n-Lie algebras . (Russian) Algebra i Logika 26 ( 3 ): 277 – 297 , 398 .
   Google Scholar
• Kornyak , V. V. ( 2000 ). Computation of cohomology of Lie superalgebras of vector fields . Internat. J. Modern Phys. C 11 2 : 397 – 413 .
   Google Scholar
• Lin , J. , Wang , Y. , Deng , S. Q. ( 2009 ). T*-extension of Lie triple systems . Linear Algebra Appl. 431 ( 11 ): 2071 – 2083 .
   Web of Science ®Google Scholar
• Ling , W. X. ( 1993 ). On the Structure of n-Lie Algebras. PhD thesis, Siegen .
   Google Scholar
• Liu , W. L. , Zhang , Z. X. ( 2012 ). T*-extension of a 3-Lie algebra . Linear and Multilinear Algebra 60 ( 5 ): 583 – 594 .
   Web of Science ®Google Scholar
• Liu , W. L. , Zhang , Z. X. ( 2013 ). T*-extension of n-Lie algebras . Linear and Multilinear Algebra 61 ( 4 ): 527 – 542 .
   Web of Science ®Google Scholar
• Medina , A. , Revoy , P. ( 1985 ). Algèbres de Lie et produit scalaire invariant . (French) Ann. Sci. École Norm. Sup. (4) 18 ( 3 ): 553 – 561 .
   Google Scholar
• Papadopoulos , G. (2008). M2-branes, 3-Lie algebras and Plücker relations. J. High Energy Phys. 054(5):9.
   Google Scholar
• Scheunert , M. , Zhang , R. B. ( 1998 ). Cohomology of Lie superalgebras and their generalizations . J. Math. Phys. 39 ( 9 ): 5024 – 5061 .
   Web of Science ®Google Scholar
• Yamaguti , K. ( 1960 ). On the cohomology space of Lie triple system . Kumamoto J. Sci. Ser. A ( 5 ): 44 – 52 .
   Google Scholar
• Communicated by M. Bresar.
   Google Scholar