摘要 : One of the main problems in PI-theory is to prove the rationality of the Hilbert series of the relatively free algebra of a given PI-algebra. In this paper we consider a field F of characteristic 0 and we prove the rationality of ... 展开 One of the main problems in PI-theory is to prove the rationality of the Hilbert series of the relatively free algebra of a given PI-algebra. In this paper we consider a field F of characteristic 0 and we prove the rationality of the Hilbert series of the PI-algebra A over F both in the case A is a superalgebra with superinvolution and when a finite dimensional semisimple Hopf algebra acts on A. Along the way, we give a proof of the Specht's problem in case A is a superalgebra with superinvolution. (c) 2021 Elsevier Inc. All rights reserved. 收起