  Connections on a trivial bundle MxG can be identified with their holonomy
maps, i.e. with homomorphisms of a groupoid of paths in M into the gauge group
G.
  For a connected compact G, various algebras depending on the set of the
smooth connections through their holonomy maps have been introduced in the
literature, called cylindrical and holonomy algebras. We discuss the relations
between these algebras and the consistence of their spectra.
