ABSTRACT

In this chapter we turn to a sublime connection, first exploited by Regev, of Pi-theory with classical representation theory (via the group algebra F[Sn]), leading to many interesting results (including Regev's exponential bound theorem). Perhaps the key result of this chapter, discovered independently by Amitsur-Regev and Kemer, shows in characteristic 0 that any Pi-algebra satisfies a sparse identity. This is the key hypothesis in translating identities to affine superidentities in Chapter 6, leading to Kemer's solution of Specht's problem.