Para-\(f\)-Lie groups. (Q1415171)

A para-\(f\)-structure on a manifold \(M\) is given by a tensor field \(\varphi\) of type \((1,1)\) of constant rank on \(M\) satisfying \(\varphi^3-\varphi=0\). Such structures have been investigated by the author in \textit{A. Bucki} [Tensor, New Ser. 48, No. 1 36--45 (1989; Zbl 0704.53025)]. In this paper the author studies special para-\(f\)-structures on Lie groups and proves that if \(G\) is a Lie group with a bi-invariant para-\(f\)-structure \(\varphi\) then \(G\) is the quotient of the product of an almost product Lie group and a Lie group with trivial para-\(f\)-structure by a discrete subgroup.