Automorphisms of the category of free Lie algebras
نویسندگان
چکیده
منابع مشابه
Automorphisms of the category of free Lie algebras
We prove that every automorphism of the category of free Lie algebras is a semi-inner automorphism. This solves the problem 3.9 from [19] for Lie algebras.
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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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Each matrix A in GLn(Z) naturally defines an automorphism f of the free r-step nilpotent Lie algebra fn,r. We study the relationship between the matrix A and the eigenvalues and rational invariant subspaces for f. We give applications to the study of Anosov automorphisms.
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An automorphism σ of a simple finite dimensional complex Lie algebra g is called torsion, if σ has finite order in the group Aut(g) of all automorphisms of g. The torsion automorphisms of g were classified by Victor Kac in [12], as an application of his results on infinite dimensional Lie algebras. Those torsion automorphisms contained in the identity component G = Aut(g)◦ are called inner; the...
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In this paper, the problem formulated in [8] is solved. We prove, that the group of automorphisms of the category of free associative algebras is generated by semi-inner and mirror automorphisms.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2004
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2003.09.038