\title{Periodic Lie modules}

\author{Kay Jin Lim}
\address[K. J. Lim]{Division of Mathematical Sciences, Nanyang Technological University, SPMS-MAS-03-01, 21 Nanyang Link, Singapore 637371.}
	
\author{Kai Meng Tan}
\address[K. M. Tan]{Department of Mathematics, National University of Singapore, Block S17, 10 Lower Kent Ridge Road, Singapore 119076.}

\begin{abstract}
Let $p$ be a prime number and $k$ be a positive integer not divisible by $p$. We describe the Heller translates of the periodic Lie module $\Lie(pk)$ in characteristic $p$ and show that it has period $2p-2$ when $p$ is odd and $1$ when $p=2$.
\end{abstract}

\thanks{We thank Karin Erdmann for providing the arguments for Proposition \ref{P:just}. We are supported by Singapore Ministry of Education AcRF Tier 1 grants RG13/14 and %. The second author is supported by Singapore Ministry of Education Academic Research Fund
R-146-000-172-112 respectively.}