  We define generalized cluster states based on finite group algebras in
analogy to the generalization of the toric code to the Kitaev quantum double
models. We do this by showing a general correspondence between systems with CSS
structure and finite group algebras, and applying this to the cluster states to
derive their generalization. We then investigate properties of these states
including their PEPS representations, global symmetries, and relationship to
the Kitaev quantum double models. We also discuss possible applications of
these states.
