Abstract. Broué and Rickard defined in their landmark papers from 1990 and 1996 the notions of an isotypy and a splendid equivalence between p-blocks of finite groups. Here, we define a notion of equivalence, which we call a ppermutation equivalence, that implies an isotypy and is implied by a splendid equivalence. Moreover, we study properties of p-permutation equivalences.
In this paper we present a necessary and sufficient condition under which a (combinatorial) morphism between association schemes induces an algebra homomorphism between their scheme rings. We will also discuss scheme ring homomorphisms of naturally valenced association schemes.
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