%0 Journal Article %T On Free Pseudo-Product Fundamental Graded Lie Algebras %A Tomoaki Yatsui %J Symmetry, Integrability and Geometry : Methods and Applications %D 2012 %I National Academy of Science of Ukraine %X In this paper we first state the classification of the prolongations of complex free fundamental graded Lie algebras. Next we introduce the notion of free pseudo-product fundamental graded Lie algebras and study the prolongations of complex free pseudo-product fundamental graded Lie algebras. Furthermore we investigate the automorphism group of the prolongation of complex free pseudo-product fundamental graded Lie algebras. %K fundamental graded Lie algebra %K prolongation %K pseudo-product graded Lie algebra %U http://dx.doi.org/10.3842/SIGMA.2012.038