Abelian ideals and cohomology of symplectic type

Li Luo

doi:10.1090/S0002-9939-08-09685-8

Abelian ideals and cohomology of symplectic type

Li Luo^*

^*Corresponding author for this work

CAS - Academy of Mathematics and System Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let b be a Borel subalgebra of the symplectic Lie algebra sp(2n, ℂ) and let n be the corresponding maximal nilpotent subalgebra. We find a connection between the abelian ideals of b and the cohomology of n with trivial coefficients. Using this connection, we are able to enumerate the number of abelian ideals of b with given dimension via the Poincaré polynomials of Weyl groups of types A_n-1 and C_n.

Original language	English
Pages (from-to)	479-485
Number of pages	7
Journal	Proceedings of the American Mathematical Society
Volume	137
Issue number	2
DOIs	https://doi.org/10.1090/S0002-9939-08-09685-8
State	Published - Feb 2009
Externally published	Yes

Keywords

Abelian ideal
Cohomology
Poincaré polynomial
Symplectic Lie algebra
Weyl group

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10.1090/S0002-9939-08-09685-8

Cite this

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AB - Let b be a Borel subalgebra of the symplectic Lie algebra sp(2n, ℂ) and let n be the corresponding maximal nilpotent subalgebra. We find a connection between the abelian ideals of b and the cohomology of n with trivial coefficients. Using this connection, we are able to enumerate the number of abelian ideals of b with given dimension via the Poincaré polynomials of Weyl groups of types An-1 and Cn.

KW - Abelian ideal

KW - Cohomology

KW - Poincaré polynomial

KW - Symplectic Lie algebra

KW - Weyl group

UR - https://www.scopus.com/pages/publications/77950527703

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DO - 10.1090/S0002-9939-08-09685-8

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JF - Proceedings of the American Mathematical Society

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ER -

Abelian ideals and cohomology of symplectic type

Abstract

Keywords

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