On ad-nilpotent b-ideals for orthogonal Lie algebras

Li Li Liu; Li Luo

doi:10.1007/s10114-012-1599-5

On ad-nilpotent b-ideals for orthogonal Lie algebras

Li Li Liu
, Li Luo

School of Mathematical Sciences

East China Normal University

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

Abstract

Krattenthaler, Orsina and Papi provided explicit formulas for the number of ad-nilpotent ideals with fixed class of nilpotence of a Borel subalgebra of a classical Lie algebra. Especially for types A and C they obtained refined results about these ideals with not only fixed class of nilpotence but also fixed dimension. In this paper, we shall follow their algorithm to determine the enumeration of ad-nilpotent b-ideals with fixed class of nilpotence and dimension for orthogonal Lie algebras, i. e., types B and D.

Original language	English
Pages (from-to)	241-262
Number of pages	22
Journal	Acta Mathematica Sinica, English Series
Volume	29
Issue number	2
DOIs	https://doi.org/10.1007/s10114-012-1599-5
State	Published - Feb 2013

Keywords

Borel subalgebra
Orthogonal Lie algebra
ad-nilpotent ideal

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10.1007/s10114-012-1599-5

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abstract = "Krattenthaler, Orsina and Papi provided explicit formulas for the number of ad-nilpotent ideals with fixed class of nilpotence of a Borel subalgebra of a classical Lie algebra. Especially for types A and C they obtained refined results about these ideals with not only fixed class of nilpotence but also fixed dimension. In this paper, we shall follow their algorithm to determine the enumeration of ad-nilpotent b-ideals with fixed class of nilpotence and dimension for orthogonal Lie algebras, i. e., types B and D.",

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AU - Luo, Li

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AB - Krattenthaler, Orsina and Papi provided explicit formulas for the number of ad-nilpotent ideals with fixed class of nilpotence of a Borel subalgebra of a classical Lie algebra. Especially for types A and C they obtained refined results about these ideals with not only fixed class of nilpotence but also fixed dimension. In this paper, we shall follow their algorithm to determine the enumeration of ad-nilpotent b-ideals with fixed class of nilpotence and dimension for orthogonal Lie algebras, i. e., types B and D.

KW - Borel subalgebra

KW - Orthogonal Lie algebra

KW - ad-nilpotent ideal

UR - https://www.scopus.com/pages/publications/84871953151

U2 - 10.1007/s10114-012-1599-5

DO - 10.1007/s10114-012-1599-5

M3 - 文章

AN - SCOPUS:84871953151

SN - 1439-8516

VL - 29

SP - 241

EP - 262

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 2

ER -

On ad-nilpotent b-ideals for orthogonal Lie algebras

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Keywords

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