Some New Polynomial Identities In Bracket Algebra

In this thesis,we find 9 new polynomial identities for bracket algebras by using the main tool,the composition algorithm,in the Gr(?)bner-Shirshov basis theory of algebras.Our method is,for the 5 of these new identities,we directly use the composition algorithm.For the other 4 identities,we first compute some compositions,then we conjecture general identities,and finally we proved these general identities by using induction.