ABSTRACT
Jose´ de Jesu´s Cruz Guzma´n and Zbigniew Oziewicz Universidad Nacional Auto´noma de Me´xico, Facultad de Estudios Superiores Cuautitla´n, Me´xico
Abstract Nonassociative Nijenhuis-Richardson graded algebra on universal module over Grassmann algebra of differential forms allows a novel and algorithmic definition of the Fro¨licher-Nijenhuis Lie R-algebra. Some consequences are derived. The signature of the five-dimensional Frobenius subalgebra of the Nijenhuis-Richardson algebra is calculated. Keywords: universal Grassmann module, Nijenhuis-Richardson algebra, Fro¨licher-Nijenhuis Lie module, Leibniz algebra, Frobenius algebra. 2000 MSC: Primary 16W25 derivation; Secondary 17A32 Leibniz algebra, 16W30 coalgebra, bialgebra.
