The Universal Central Extensions Of LPNG Algebra

Commutative associative algebras are a class of common algebras,Lie algebras play an important rolein the forward fields of modern mathematics , which include many nice results.Novikov algebras are appliedin physics and mathematics,it also play an important role in solving Yang-Baxter equations. LPNG algebrais defined on the basis of commutative associative algebra,Lie algebra and Novikov algebra, it has threealgebraic structure and satisfies four compatibility conditions, certain two algebraic between it can sepa-rately formed Novikov-Poisson algebras and Gel'fand-Dorfman algebras. In the second section we givethe definition ,subalgebra , ideal and other basic definitions of LPNG algebra.In the third section we givethe examples of LPNG algebra.In the forth section we study the central extensions and universal centralextensions of LPNG algebra, we obtain the universal covering of LPNG algebra A is exist if and only if A isperfect. In the last section we acquire the conditions of lifting automorphisms and derivations.