Abstract. In this work, we describe a method to construct central polynomials for F -algebras where F is a field of characteristic zero. The main application deals with the T -prime algebras Mn(E), where E is the infinite-dimensional Grassmann algebra over F , which play a fundamental role in the theory of PI-algebras. The method is based on the explicit decomposition of the group algebra F Sn.
The main goal of this paper is to prove that the five algebras which were used in [3] to classify (up to PI-equivalence) the algebras whose sequence of codimensions is bounded by a linear function generate the only five minimal varieties of quadratic growth.
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