\title{The Non-Projective Part of the tensor powers of a module}

\author{Dave Benson}
\address{Institute of Mathematics, University of Aberdeen, Aberdeen
  AB24 3UE, Scotland, United Kingdom}

\author{Peter Symonds}
\address{School of Mathematics, University of Manchester, 
Oxford Road, Manchester M13 9PL, United Kingdom}

\keywords{Projective module, core, tensor powers, modular
  representation, Green ring, commutative Banach algebra}

\subjclass[2010]{20C20, 46J99}

\begin{document}

\maketitle

\begin{abstract}
Let $M$ be a finite dimensional modular representation of
a finite group $G$. We consider the generating function for the
non-projective part of the tensor powers of $M$, and we
write $\npj_G(M)$ for the reciprocal of the radius of convergence
of this power series. We investigate the properties of the
invariant $\npj_G(M)$, using tools from representation theory,
and from the theory of commutative Banach algebras. 
\end{abstract}