On Eigenvectors of Nilpotent Lie Algebras of Linear Operators
نویسندگان
چکیده
We give a condition ensuring that the operators in nilpotent Lie algebra of linear on finite dimensional vector space have common eigenvector.
منابع مشابه
On Eigenvectors of Nilpotent Lie Algebras of Linear Operators
We give a condition ensuring that the operators in a nilpotent Lie algebra of linear operators on a finite dimensional vector space have a common eigenvector. Introduction Throughout this paper V is a vector space of positive dimension over a field f and g is a nilpotent Lie algebra over f of linear operators on V . An element u ∈ V is an eigenvector for S ⊂ g if u is an eigenvector for every o...
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نشان می دهیم که هر اشتقاق لی روی یک c^*-جبر به شکل استاندارد است، یعنی می تواند به طور یکتا به مجموع یک اشتقاق لی و یک اثر مرکز مقدار تجزیه شود. کلمات کلیدی: اشتقاق، اشتقاق لی، c^*-جبر.
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In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.
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ژورنال
عنوان ژورنال: European Journal of Pure and Applied Mathematics
سال: 2021
ISSN: ['1307-5543']
DOI: https://doi.org/10.29020/nybg.ejpam.v14i4.4086