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On the adjoint homology of 2-step nilpotent Lie algebras

Published online by Cambridge University Press:  17 April 2009

Leandro Cagliero
Affiliation:
CIEM-FaMAF, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina, e-mail: cagliero@mate.uncor.edu, ptirao@mate.uncor.edu
Paulo Tirao
Affiliation:
CIEM-FaMAF, Universidad Nacional de Córdoba, 5000 Córdoba, Argentina, e-mail: cagliero@mate.uncor.edu, ptirao@mate.uncor.edu
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We give a lower bound and an upper bound for the dimension of the homology of 2-step nilpotent Lie algebras with adjoint coefficients. We conjecture, that the upper bound and the actual dimension are asymptotically equivalent.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Cagliero, L. and Tirao, P., ‘The adjoint homology of the free 2-step nilpotent Lie algebra’, Q.J. Math. 53 (2002), 125145.Google Scholar
[2]Cagliero, L. and Tirao, P., ‘The cohomology of the cotangent bundle of Heisenberg groups’, Adv. Math. 181 (2004), 276307.Google Scholar
[3]Dixmier, J., ‘Cohomologie des algèbres de Lie nilpotentes’, Acta Sci. Math. 16 (1955), 246250.Google Scholar
[4]Grassberger, J., King, A. and Tirao, P., ‘On the homology of free 2-step nilpotent Lie algebras’, J. Algebra 254 (2002), 213225.Google Scholar
[5]Magnin, L., ‘Cohomologie adjointe des algèbres de Lie de Heisenberg’, Comm. Algebra 21 (1993), 21012129.CrossRefGoogle Scholar
[6]Santharoubane, L.J., ‘Cohomology of Heisenberg Lie algebras’, Proc. Amer. Math. Soc. 87 (1983), 2328.Google Scholar
[7]Tirao, P., ‘A refinement of the Toral Rank Conjecture for 2-step nilpotent Lie algebras’, Proc. Amer. Math. Soc. 128 (2000), 28752878.Google Scholar