Degeneracy points in non-Hermitian systems are of great interest. While a homotopic framework exists for understanding their behavior in the absence of symmetry, it does not apply to symmetry-protected degeneracy points with reduced codimension. In this work, utilizing algebraic topology, we provide a systematic classification of these symmetry-protected degenerate points and investigate the braid conservation rule followed by them. Using a model Hamiltonian and circuit simulation, we discover that, contrary to simple annihilation, pairwise-created symmetry-protected degeneracy points merge into a higher-order degeneracy point, which goes beyond the abelian picture. Our findings empower researchers across diverse fields to uncover new phenomena and applications harnessing symmetry-protected non-Hermitian degeneracy points.

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• Geometric & topological phases
• Non-Hermitian systems
• Abstract algebra
• Symmetries in condensed matter
• Topology