The Double Derivations Of Twisted Heisenberg-Virasoro Algebras And Their Applications

In this paper,the biderivations without the skew-symmetric condition of the twisted Heisenberg-Virasoro algebra are presented.We find some non-inner and non-skew-symmetric biderivations.As applications,the characterizations of the forms of linear commuting maps and the commutative post-Lie algebra structures on the twisted Heisenberg-Virasoro algebra are given.It also is proved that every biderivation of the graded twisted Heisenberg-Virasoro left-symmetric algebra is trivial.In Chapter 1,we mainly introduces the research background,the research status at home and abroad,the development trend,the purpose and significance of this paper,such as biderivations,inner biderivation.In Chapter 2,we give some preliminary knowledge,mainly related to the basic concepts of this paper.In chapter 3,we have study the biderivation of the twisted Heisenberg-Virasoro algebra,then prove that the biderivation of the twisted Heisenberg-Virasorol algebra are non-inner.In chapter 4,as an application,the structures of post lie algebra and bideriva-tion of left-symmetric algebras on the twisted Heisenberg-Virasoro algebra are given.