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An algebra $L$ over a field $\Bbb F$, in which product is denoted by$[\,,\,]$, is said to be \textit{ Lie type algebra} if for all elements$a,b,c\in L$ there exist $\alpha, \beta\in \Bbb F$ such that $\alpha\neq 0$ and$[[a,b],c]=\alpha [a,[b,c]]+\beta[[a,c],b]$. Examples of Lie type algebras areassociative algebras, Lie algebras, Leibniz algebras, etc. It is proved that ifa Lie type algebra $L$ admits an automorphism of finite order $n$ withfinite-dimensional fixed-point subalgebra of dimension $m$, then $L$ has asoluble ideal of finite codimension bounded in terms of $n$ and $m$ and ofderived length bounded in terms of $n$.

Lie type algebras with an automorphism of finite order