Flat Hypercomplex Nilmanifolds are \(\mathbb H\)-Solvable

IF 0.6 4区 数学 Q3 MATHEMATICS
Yulia Gorginyan
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引用次数: 0

Abstract

Let \(\mathbb H\) be a quaternion algebra generated by \(I,J\) and \(K\). We say that a hypercomplex nilpotent Lie algebra \(\mathfrak g\) is \(\mathbb H\)-solvable if there exists a sequence of \(\mathbb H\)-invariant subalgebras containing \(\mathfrak g_{i+1}=[\mathfrak g_i,\mathfrak g_i]\),

such that \([\mathfrak g_i^{\mathbb H},\mathfrak g_i^{\mathbb H}]\subset\mathfrak g^{\mathbb H}_{i+1}\) and \(\mathfrak g_{i+1}^{\mathbb H}=\mathbb H[\mathfrak g_i^{\mathbb H},\mathfrak g_i^{\mathbb H}] \). Let \(N=\Gamma\setminus G\) be a hypercomplex nilmanifold with the flat Obata connection and \(\mathfrak g=\operatorname{Lie}(G)\). We prove that the Lie algebra \(\mathfrak g\) is \(\mathbb H\)-solvable.

平超复数无穷折线是(\mathbb H\ )可解的
让 \(\mathbb H\) 是一个由 \(I,J\) 和 \(K\) 生成的四元数代数。如果存在一个包含 \(\mathfrak g_{i+1}=[\mathfrak g_i,\mathfrak g_i]\)的 \(\mathbb H\)-invariant 子代数序列,那么我们说一个超复数零能烈代数是 \(\mathbb H\)-solvable 的、 使得([\mathfrak g_i^{\mathbb H}、\和(\mathfrak g_{i+1}^{\mathbb H}=\mathbb H[\mathfrak g_i^{\mathbb H},\mathfrak g_i^{\mathbb H}] \)。让(N=\Gamma\setminus G\) 是一个具有平面小畑(Obata)连接的超复数无芒点,并且(\mathfrak g=\operatorname{Lie}(G)\)是一个具有平面小畑(Obata)连接的超复数无芒点。我们证明了烈代数((\mathfrak g\) is \(\mathbb H\) -solvable.
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
7
审稿时长
>12 weeks
期刊介绍: Functional Analysis and Its Applications publishes current problems of functional analysis, including representation theory, theory of abstract and functional spaces, theory of operators, spectral theory, theory of operator equations, and the theory of normed rings. The journal also covers the most important applications of functional analysis in mathematics, mechanics, and theoretical physics.
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