Journal of the
Korean Mathematical Society JKMS

By developing a linear algebra program involving many different structures associated to a three-graded $H^*$-algebra, it is shown that if $L$ is a Lie triple automorphism of an infinite-dimensional topologically simple associative $H^*$-algebra $A$, then $L$ is either an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism. If $A$ is finite-dimensional, then there exists an automorphism, an anti-automorphism, the negative of an automorphism or the negative of an anti-automorphism $F:A \to A$ such that $\delta:=F-L$ is a linear map from $A$ onto its center sending commutators to zero. We also describe $L$ in the case of having $A$ zero annihilator.

Keywords: $H^*$-algebra, graded algebra, Jordan pair, Lie triple automorphism

MSC numbers: 17B40, 46L40, 47B47, 46K70