  The group structure of the variant chiral symmetry discovered by Luscher in
the Ginsparg-Wilson description of lattice chiral fermions is analyzed. It is
shown that the group contains an infinite number of linearly independent
symmetry generators, and the Lie algebra is given explicitly. CP is an
automorphism of this extended chiral group, and the CP transformation
properties of the symmetry generators are found. The group has an
infinite-parameter invariant subgroup, and the factor group, whose elements are
its cosets, is isomorphic to the continuum chiral symmetry group. Features of
the currents associated with these symmetries are discussed, including the fact
that some different, non-commuting symmetry generators lead to the same Noether
current. These are universal features of lattice chiral fermions based on the
Ginsparg-Wilson relation; they occur in the overlap, domain-wall, and
perfect-action formulations. In a solvable example, free overlap fermions,
these non-canonical elements of lattice chiral symmetry are related to complex
energy singularities that violate reflection positivity and impede continuation
to Minkowski space.
