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Lie rings admitting an automorphism of order 4 with few fixed points. (English. Russian original) Zbl 0903.17008

Algebra Logika 37, No. 2, 144-166 (1998); translation in Algebra Logic 37, No. 2, 78-91 (1998).
In the article, the following theorem is proven. Theorem. If a Lie ring (algebra) \(L\) admits an automorphism of order 4 with a finite number \(m\) of fixed points (with the subalgebra of fixed points having finite dimension \(m\)) then \(L\) has a subring \(S\) of \(m\)-bounded index in the additive group \(L\) (a subalgebra \(S\) of \(m\)-bounded codimension) possessing a nilpotent ideal \(I\) of degree bounded by some constant such that the quotient ring \(S/I\) is nilpotent of degree \(\leq 2\).

MSC:

17B40 Automorphisms, derivations, other operators for Lie algebras and super algebras

Citations:

Zbl 0896.17005
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