学术报告题目与摘要
（按报告出场顺序）
On vector bundles of rank two on a weighted projective line
阮诗佺
清华大学
This is joint work with Helmut Lenzing.This survey is a remark on the paper
“Triangle singularities, ADE-chains and weighted projective lines” authored by
Kussin,Lenzing and Meltzer.
All the major results there are based on the features of
extension bundles, that is, indecomposable vector bundles of rank two. We continue to
investigate extension bundles on a weighted projective line of weight triple. We
describe when these bundles are in the same orbit under line bundle twist. Basing on
this observation, the exact number of the orbits of extension bundles is given.
Moreover, we also show some interesting results on tilting objects that are consisting
of extension bundles in the stable category of vector bundles.
代数的量（magnitude）
陈正新
福建师范大学
计算出有限维遗传代数、法式代数、管子代数的量，研究有限维代数的量在
单点扩张、倾斜过程中的不变性。
monomial 代数的平凡扩张
蔡毓麟
厦门大学
利用相应的底图和关系刻画 monomial 代数的平凡扩张代数, 并用此给出
monomial 代数到其平凡扩张代数 Loewy 长度的公式。
Mutation pairs and n-angulated quotients
林增强
华侨大学
We define mutation pairs in n-angulated categories and prove that given such a
mutation pair, the corresponding quotient category carries a natural n-angulated
structure. This result generalizes a theorem of Iyama-Yoshino for triangulated
categories.
Monadicity Theorem and Weighted Projective Lines of Tubular Type
陈健敏
厦门大学
We formulate a version of Beck's monadicity theorem for abelian categories, which is
applied to the equivariantization of an abelian category with respect to a finite group action. We
prove that the equivariantization is compatible with the construction of quotient abelian categories
by Serre subcategories. We prove that the equivariantization of the graded module category over a
graded ring is equivalent to the graded module category over the same ring but with a different
grading. We deduce from these results two equivalences between the category of (equivariant)
coherent sheaves on a weighted projective line of tubular type and that on an elliptic curve, where
the acting groups are cyclic and the two equivalences are adjoint to each other. This is joint with
Xiao-Wu Chen and Zhenqiang Zhou.
K-理论的简介
郑敏
福建师范大学
环的 K0-群的四种等价定义以及环的 K1-群的两种等价定义，简单阐述了 Ki群的基本性质, 给出一些特殊环类的 Ki 群的刻划(i=0,1)。
Matrix Pairs whose Sum is Equal to Product and Generalized
Quadratic Matrices
陈梅香
福建师范大学
In 2005, Farebrother R W , Trenkler G. introduced the definition of a generalized
quadratic matrix, including the quadratic matrices. For a matrix pair A, B whose sum
is equal to product and an idempotent matrix P , we prove that B is a generalized
quadratic matrix determined by P if and only if A is also a generalized quadratic
matrix determined by P ; meanwhile, we also obtain the sufficient and necessary
conditions for matrix equation AX = A + X having a solution of generalized
quadratic matrix.
三角范畴的 n-silting 对象及其应用
刘宏锦
福建师范大学
研究带有 serre 函子的三角范畴，定义三角范畴的 n-silting 对象，利用其构
造(n+1)-倾斜子范畴。