  On the one hand the algebras of linear operators here act on
finite-dimensional vector spaces, and on the other hand the point of view is
generally an analysts'. Also, one might think of algebras as being used to add
more data to basic geometry as on a graph, for instance. Of course this is a
common theme which is considered in numerous settings. From an analysts'
perspective, compact groups, their representations, and more general
topological groups and their representations are basic objects of study. Finite
groups are like groups which are especially compact, and with some extra
structure. As long as one considers finite groups and finite-dimensional vector
spaces, one might as well consider general underlying fields k too. This
includes p-adic fields, which are quite interesting for analysis.
