Vol. 82, No. 1, 1979

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On unitary automorphisms of solvable Lie algebras

Oldřich Kowalski

Vol. 82 (1979), No. 1, 133–143

Let V be a finite dimensional vector space over real numbers. An automorphism A of V is called unitary if it is semisimple and all its eigenvalues are complex units. Particularly, all periodic automorphisms, i.e., such that Tk = identity for some integer k, are unitary. The aim of this paper is to prove the following Theorem. Let g be an n-dimensional real Lie algebra admitting a unitary automorphism without nonzero fixed vectors. Then g admits a periodic automorphism without nonzero fixed vectors and of order k, where k 5n∕4 for n even, and k 2.5(n1)4 for n odd.

Mathematical Subject Classification 2000
Primary: 17B40
Received: 14 August 1975
Revised: 21 December 1978
Published: 1 May 1979
Oldřich Kowalski