Abelian ideals and cohomology of symplectic type

Author:
Li Luo

Journal:
Proc. Amer. Math. Soc. **137** (2009), 479-485

MSC (2000):
Primary 17B05, 17B56; Secondary 17B20, 17B30

DOI:
https://doi.org/10.1090/S0002-9939-08-09685-8

Published electronically:
September 29, 2008

MathSciNet review:
2448567

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Borel subalgebra of the symplectic Lie algebra and let be the corresponding maximal nilpotent subalgebra. We find a connection between the abelian ideals of and the cohomology of with trivial coefficients. Using this connection, we are able to enumerate the number of abelian ideals of with given dimension via the Poincaré polynomials of Weyl groups of types and .

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Additional Information

**Li Luo**

Affiliation:
Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Email:
luoli@amss.ac.cn

DOI:
https://doi.org/10.1090/S0002-9939-08-09685-8

Keywords:
Abelian ideal,
cohomology,
symplectic Lie algebra,
Weyl group,
Poincar\'e polynomial.

Received by editor(s):
January 24, 2008

Published electronically:
September 29, 2008

Communicated by:
Gail R. Letzter

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.