Exceptional isomorphism

In mathematics, an exceptional isomorphism, also called an accidental isomorphism, is an isomorphism between members a_i and b_j of two families, usually infinite, of mathematical objects, which is incidental, in that it is not an instance of a general pattern of such isomorphisms. These coincidences are at times considered a matter of trivia, but in other respects they can give rise to consequential phenomena, such as exceptional objects. In the following, coincidences are organized according to the structures where they occur.