  Despite recent extensive studies of the non-Hermitian topology, understanding
interaction effects is left as a crucial question. In this paper, we address
interaction effects on exceptional points which are protected by the
non-trivial point-gap topology unique to non-Hermitian systems. Our analysis in
a two-dimensional parameter space elucidates the existence of exceptional
points and symmetry-protected exceptional rings fragile against interactions;
they are topologically protected only in non-interacting cases. This fragility
of exceptional points and symmetry-protected exceptional rings arises from the
reduction of non-Hermitian topological classifications, which is elucidated by
introducing topological invariants of the second-quantized Hamiltonian for both
non-interacting and interacting cases. These topological invariants are also
available to analyze the reduction phenomena of gapped systems. The above
results strongly suggest similar reduction phenomena of exceptional points in
generic cases and open up a new direction of research in the non-Hermitian
topology.
