Biderivations And Left-symmetric Algebra Structures On The Deformed Bms₃ Algebra

In this thesis,we mainly study the structure of the deformed bms₃ algebra.The deformed bms₃ algebra is obtained as an S-expansion of the Virasoro algebra.It is known that the Vi-rasoro algebra has been studied in the range of structures and representations in recent years Based on these,we study biderivations,linear commuting maps and left-symmetric algebra structures on the deformed bms₃ algebra.There are three chapters,as followsIn the first chapter,it is the introduction,which is divided into three sections.The back-ground of the research is introduced in the first section.In the second section,we give some basic knowledge.In order to simplify the writing,we give the symbol descriptions in the third sectionThere are three sections in the second chapter,we mainly study the biderivations and lin-ear commuting maps on the deformed bms₃ algebra.In Section 1,to lay a steady foundation for the next work,we mainly introduce some basic concepts and general conclusions.In Section 2,we determine that not all the skew-symmetric biderivations of the deformed bms₃ algebra are inner biderivations.Finally,in the last section,based on the result of skew-symmetric bideriva-tions,we will give the form of each linear commuting map on the deformed bms₃ algebra,that is,they are standardIn the third chapter,we mainly determine the compatible left-symmetric algebra struc-tures on the deformed bms₃ algebra with some natural grading conditions.This chapter is simply divided into two sections.In Section 1,we give the basic concepts and the results about left-symmetric algebra structure.And we give the main results of this chapter.In the first subsection of Section 2,we classify the left-symmetric algebra structures on the centerless deformed bms₃ algebra under certain natural assumptions.In the second subsection of Section 2,we determine the nontrivial central extensions of the left-symmetric algebras on the basis of the previous subsection.