Thomae’s function on a Lie group

IF 0.7 3区 数学 Q2 MATHEMATICS Pacific Journal of Mathematics Pub Date : 2021-07-31 DOI:10.2140/pjm.2023.322.139
Mark Reeder
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引用次数: 2

Abstract

Let $\mathfrak g$ be a simple complex Lie algebra of finite dimension. This paper gives an inequality relating the order of an automorphism of $\mathfrak g$ to the dimension of its fixed-point subalgebra, and characterizes those automorphisms of $\mathfrak g$ for which equality occurs. This is amounts to an inequality/equality for Thomae's function on the group of automorphisms of $\mathfrak g$. The result has applications to characters of zero weight spaces, graded Lie algebras, and inequalities for adjoint Swan conductors.
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李群上的托马函数
设$\ mathfrakg $是一个有限维的简单复李代数。本文给出了$\mathfrak g$的自同构的阶与其不动点子代数维数之间的一个不等式,并刻画了$\mathfrak g$的自同构存在相等的性质。这相当于在$\mathfrak g$的自同构群上的thomas函数的不等式/等式。该结果可应用于零权空间的性质、梯度李代数和伴随Swan导体的不等式。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
1.30
自引率
0.00%
发文量
93
审稿时长
4-8 weeks
期刊介绍: Founded in 1951, PJM has published mathematics research for more than 60 years. PJM is run by mathematicians from the Pacific Rim. PJM aims to publish high-quality articles in all branches of mathematics, at low cost to libraries and individuals. The Pacific Journal of Mathematics is incorporated as a 501(c)(3) California nonprofit.
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