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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Abelian ideals and cohomology of symplectic type
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by Li Luo PDF
Proc. Amer. Math. Soc. 137 (2009), 479-485 Request permission

Abstract:

Let $\mathfrak {b}$ be a Borel subalgebra of the symplectic Lie algebra $\mathfrak {sp}(2n,\mathbb {C})$ and let $\mathfrak {n}$ be the corresponding maximal nilpotent subalgebra. We find a connection between the abelian ideals of $\mathfrak {b}$ and the cohomology of $\mathfrak {n}$ with trivial coefficients. Using this connection, we are able to enumerate the number of abelian ideals of $\mathfrak {b}$ with given dimension via the Poincaré polynomials of Weyl groups of types $A_{n-1}$ and $C_n$.
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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
  • Received by editor(s): January 24, 2008
  • Published electronically: September 29, 2008
  • Communicated by: Gail R. Letzter
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2448567