Generalized Derivations And (σ,τ )-derivations On Novikov Superalgebras

A Novikov superalgebra is a natural generalization of a Novikov algebra.Novikov superalgebras are closely related to conformal superalgebras and vertex operator superalgebras,and have important applications in quantum field theory and integrable systems.This thesis mainly studies generalized derivations,(σ,τ)-derivations and derivation structures of Novikov superalgebras.It consists of four chapters.Chapter 1 is introduction.Firstly,the development of Novikov algebras and Novikov superalgebras is briefly introduced,and some research results of domestic and foreign scholars in recent years are listed.Then some related results of derivations and generalized derivations are introduced.Finally,the progress of(σ,τ)-derivations is introduced.Chapter 2 studies generalized derivations of Novikov superalgebras.First of all,the definitions of Novikov superalgebras,generalized derivations,central derivations,quasiderivations and their relationships are given.Then the properties of central derivations of Novikov superalgebras are studied.Finally,a semisimple quasiderivations of Novikov superalgebras with zero center and nondecomposition is described,and the equivalent characterization of quasiderivations is also given.Chapter 3 studies(σ,τ)-derivations on Novikov superalgebras.The definition of(σ,τ)-derivations of Novikov superalgebras is given and its properties are studied.Then the interior of G-derivations of Novikov superalgebras is defined,and its Hilbert series is calculated when G is an infinite cyclic group.Finally,(σ,τ)-derivations,derivations and quasi-derivations of Novikov superalgebras are studied.Chapter 4 studies derivation structures of Novikov superalgebras.The cardinal multiplication matrix is defined,and the derivation structures are calculated by the classifications of Novikov superalgebras.