Left-invariant conformal vector fields on non-solvable Lie groups,Proceedings of the American Mathematical Society

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Left-invariant conformal vector fields on non-solvable Lie groups
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-12-14 , DOI: 10.1090/proc/15272
Hui Zhang , Zhiqi Chen , Ju Tan

Abstract:Let $(G,\langle \cdot ,\cdot \rangle )$ be a pseudo-Riemannian Lie group of type

with the Lie algebra $\mathfrak{g}$ . In this paper, we prove that

is solvable if $(G,\langle \cdot ,\cdot \rangle )$ admits a non-Killing left-invariant conformal vector field and $\dim [\mathfrak{g},\mathfrak{g}]=\dim \mathfrak{g}-\min (p,q)+1$ for $\min (p,q)\geq 2$ . Then we construct a non-solvable pseudo-Riemannian Lie group

of type

which admits a non-Killing left-invariant conformal vector field and $\dim [\mathfrak{g},\mathfrak{g}]=\dim \mathfrak{g}-\min (p,q)+d$ for any $p,q\geq 3$ and $2\leq d\leq \min (p,q)-1$ . It gives a negative answer to a forthcoming conjecture by H. Zhang and Z. Chen.

中文翻译：

不可解李群上的左不变保形向量场

摘要：让具有李代数的伪黎曼李群成为一类。在本文中，我们证明，如果接受一个非杀死左不变形保形向量场，则对于，它是可解的。然后，我们构造一个不可解的伪黎曼李群，其类型允许一个非Killing的左不变保形向量场，并且适用于和。它给即将发表的H. Zhang和Z. Chen的猜想提供了否定的答案。 $（G，\ langle \ cdot，\ cdot \ rangle）$

$\ mathfrak {g}$

$（G，\ langle \ cdot，\ cdot \ rangle）$ $\ dim [\ mathfrak {g}，\ mathfrak {g}] = \ dim \ mathfrak {g}-\ min（p，q）+ 1$ $\ min（p，q）\ geq 2$

$\ dim [\ mathfrak {g}，\ mathfrak {g}] = \ dim \ mathfrak {g}-\ min（p，q）+ d$ $p，q \ geq 3$ $2 \ leq d \ leq \ min（p，q）-1$

更新日期：2021-01-11

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