Some Properties Of Jacobian Algebras

An n-Lie algebra is a natural generalization of the concept of a Lie algebra to the case where the fundamental multiplication operation is n-ary n ≥ 2 (When n = 2, the definition agrees with the usual definition of a Lie algebra), and a Jacobian algebra is an important part ofit.In this thesis, we mainly investigate some properties of A(n,t). We firstly obtain some derivations, such as D_t,(D|-)_t,Δ and so on. Secondly, we study a class of automorphisms of A(n,t), i.e., we prove that the set {φ∈SL_n(R)|φ(t) = t) is a subgroup of Aut(A(n,t)),Finally, we mainly discuss some properties of the operation w in A(n,t), i.e., g~w = 0, f~w = 0 and Leibniz identity.