\title[Examples of support varieties]
{Examples of support varieties for Hopf algebras
with noncommutative tensor products}

\author{Dave Benson}
\address{Institute of Mathematics, University of Aberdeen, King's College, 
Aberdeen AB24 3UE, Scotland, U.K.}

\author{Sarah Witherspoon}
\address{Department of Mathematics, Texas A\&M University, College Station,
Texas 77843, U.S.A.}

\date{9 July 2013}

\thanks{This material is based upon work supported by the National Science 
Foundation under Grant No.~0932078~000, while the authors were in 
residence at the Mathematical Science Research Institute (MSRI) in 
Berkeley, California, during the Spring semester of 2013.
The second author was supported by National Science Foundation Grant No.\
DMS-1101399.} 

\begin{abstract}
The representations of some Hopf algebras have  curious behavior: 
Nonprojective modules may have projective tensor powers, 
and the variety of a tensor product of modules
may not be  contained in the intersection of their varieties. 
We explain  a family of examples of such  Hopf algebras and their modules, 
and classify  left, right, and two-sided ideals in 
their stable module categories. 
\end{abstract}