THE SECOND BETTI NUMBER OF NILPOTENT JORDAN-TYPE LIE ALGEBRAS
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Abstract
In this paper, we calculate the second Betti number of nilpotent Jordan-type Lie algebras in Duong, Pinczon and Ushirobira (2012) through computing super-Poisson brackets on their algebra of multi – skew symmetric forms.
Keywords
Quadratic Lie algebras, Cohomology, super-Poisson bracket
Article Details
References
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Duong, M. T., Pinczon, G. & Ushirobira, R. (2012). A new invariant of quadratic Lie algebras. Alg. and Rep. Theory, 15(6), 1163-1203.
Favre, G., & Santharoubane, L. J. (1987). Symmetric, invariant, non-degenerate bilinear form on a Lie algebra. J. Algebra, 105, 451-464.
Figueroa-O’Farrill, J. M., & Stanciu, S. (1996). On the structure of symmetric self-dual Lie algebras. J. Math. Phys, 37, 4121-4134.
Kac, V. (1985). Infinite-dimensional Lie algebras. Cambrigde University Press, New York.
Medina, A., & Revoy, P. (1985). Algèbres de Lie et produit scalaire invariant. Ann. Sci. Éc. Norm. Sup., 4ème sér. 18, 553-561.
Pinczon, G., & Ushirobira, R. (2007). New Applications of Graded Lie Algebras to Lie Algebras, Generalized Lie Algebras, and Cohomology. J. Lie Theory, 17, 633-667.
Pouseele, H. (2005). On the cohomology of extensions by a Heisenberg Lie algebra. Bull. Austral. Math. Soc., 71, 459-470
Santharoubane, L. J. (1983). Cohomology of Heisenberg Lie algebras. Proc. Amer. Math. Soc., 87, 23-28.
Duong, M. T., Pinczon, G. & Ushirobira, R. (2012). A new invariant of quadratic Lie algebras. Alg. and Rep. Theory, 15(6), 1163-1203.
Favre, G., & Santharoubane, L. J. (1987). Symmetric, invariant, non-degenerate bilinear form on a Lie algebra. J. Algebra, 105, 451-464.
Figueroa-O’Farrill, J. M., & Stanciu, S. (1996). On the structure of symmetric self-dual Lie algebras. J. Math. Phys, 37, 4121-4134.
Kac, V. (1985). Infinite-dimensional Lie algebras. Cambrigde University Press, New York.
Medina, A., & Revoy, P. (1985). Algèbres de Lie et produit scalaire invariant. Ann. Sci. Éc. Norm. Sup., 4ème sér. 18, 553-561.
Pinczon, G., & Ushirobira, R. (2007). New Applications of Graded Lie Algebras to Lie Algebras, Generalized Lie Algebras, and Cohomology. J. Lie Theory, 17, 633-667.
Pouseele, H. (2005). On the cohomology of extensions by a Heisenberg Lie algebra. Bull. Austral. Math. Soc., 71, 459-470
Santharoubane, L. J. (1983). Cohomology of Heisenberg Lie algebras. Proc. Amer. Math. Soc., 87, 23-28.