  With some assumptions, the algebra between Ishibashi states in string field
theory can be reduced to a commutative ring. From this viewpoint, Cardy states
can be identified with its idempotents. The algebra can be identified with a
fusion ring for the rational conformal field theory and a group ring for the
orbifold. This observation supports our previous observation that boundary
states satisfy a universal idempotency relation under closed string star
product.
