m-循环复形范畴的Bridgeland-Hall代数的余代数结构

设A是一个遗传Abel范畴且■是A的投射对象构成的满子范畴.本文主要研究胁循环复形范畴C_m(■)的Bridgeland-Hall代数的余代数结构(其中m≥2).受Yanagida工作的启发,我们在C_m(■)上定义一个新的正合结构,由此得到了其Bridgeland-Hall代数的余代数结构.同时,证明了存在A的扩展Ringel-Hall代数到m-循环复形范畴C_m(■)的Bridgeland-Hall代数的余代数嵌入.

Coalgebra Structure on the Bridgeland–Hall Algebra of Categories of m-Cyclic Complexes

Let A be a hereditary abelian category and P the full subcategory consisting of projective objects of A . We mainly study the coalgebra structure on the Bridgeland–Hall algebra of the category Cm(P) of m-cyclic complexes for any positive integer m ≥ 2. Inspired by the work of Yanagida, we define a new exact structure on Cm(P) and then obtain a coalgebra structure on the Bridgeland–Hall algebra of Cm(P). Moreover, we prove that there exists a coalgebra embedding from the extended Ringel–Hall algebra of A to the Bridgeland–Hall algebra of Cm(P).