Derivation Algebras And Automorphisms Of Finite Dimensional Quotient Algebra Of The Leibniz Algebra F[x,y]

This paper discusses the derivation algebras and automorphisms of F[x,y]/In, which is the finite dimensional quotient algebra of the Leibniz algebra F[x,y]. Firstly, we have com-puted the derivation algebras of the quotient algebra F[x,y]/In when n equals1,2,3, then it is extended to the general case of n. Secondly, we have found out the automorphisms of [x,y]/I1, and some special ones of F[x,y]/In (n≥2).