A characterization of minimal varieties of Zp-graded PI algebras

Abstract Let F be a field of characteristic zero and p a prime. In the present paper it is proved that a variety of Z p -graded associative PI F-algebras of finite basic rank is minimal of fixed Z p -exponent d if, and only if, it is generated by an upper block triangular matrix algebra U T Z p ( A 1 , … , A m ) equipped with a suitable elementary Z p -grading, whose diagonal blocks are isomorphic to Z p -graded simple algebras A 1 , … , A m satisfying dim F ⁡ ( A 1 ⊕ ⋯ ⊕ A m ) = d .