Potentials for some tensor algebras

This paper generalizes former works of Derksen, Weyman and Zelevinsky about quivers with potentials. We consider semisimple finite-dimensional algebras E over a field F, such that E?FEop is semisimple. assume contains certain type F-basis which generalization multiplicative basis. study potentials belonging to the algebra formal power series, coefficients in tensor E, any E-E-bimodule on F acts centrally. In this case, we introduce cyclic derivative each potential associate Jacobian ideal. Finally, develop mutation theory potentials, case bimodule Z-free, it behaves as quiver case; but allows us obtain realizations class skew-symmetrizable integer matrices.