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On regular automorphisms of algebras. (English) Zbl 0166.03905

The author shows that if the cyclic group of order \(n\) has a non-trivial character in the field \(k\), then there is an \(n\)-dimensional simple non-associative algebra (truncated loop algebra) which has a (semi-simple) automorphism \(A\) whose fixed point set is \(\{0\}\).

MSC:

17A36 Automorphisms, derivations, other operators (nonassociative rings and algebras)
17A60 Structure theory for nonassociative algebras
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