The symbol 
used to denote multiplication, i.e., 
denotes 
times 
.
The symbol 
is also used to denote a group direct product,
a Cartesian product, or a direct product in
the appropriate category (such as a Cartesian product of manifolds when it is implied
that the smooth structure is the natural product structure.) The similar symbol 
is reserved for a tensor product,
which may rear its head in several guises, representations, bundles, modules.
