SIMPLICITY OF THE LIE ALGEBRA OF SKEW SYMMETRIC ELEMENTS OF A LEAVITT PATH ALGEBRA

摘要

For a field F of characteristic not 2 and a directed row-finite graph Gamma let L (Gamma) be the Leavitt Path Algebra with standard involution *. We study the lie algebra of K = K(L(Gamma), *) of *-skew-symmetric elements and find necessary and sufficient conditions for the Lie algebra [K, K] to be simple.