关于利玛窦的负推导

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2020-12-04 DOI:10.1515/advgeom-2022-0004

María Valeria Gutiérrez

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引用次数: 1

摘要

摘要给定一个幂零李代数，研究了所有可对角导的空间，使得相应的一维可解扩展允许一个负Ricci曲率的左不变度量。Lauret和Will推测这样的空间与幂零李代数的矩映射定义的导数的开凸子集相吻合。我们证明了这个猜想在维数≤5上的有效性，以及对于Heisenberg李代数和标准丝状李代数的有效性。

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On Ricci negative derivations

Abstract Given a nilpotent Lie algebra, we study the space of all diagonalizable derivations such that the corresponding one-dimensional solvable extension admits a left-invariant metric with negative Ricci curvature. Lauret and Will have conjectured that such a space coincides with an open and convex subset of derivations defined in terms of the moment map for the variety of nilpotent Lie algebras. We prove the validity of the conjecture in dimensions ≤ 5, as well as for Heisenberg Lie algebras and standard filiform Lie algebras.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.