k上G-分次范畴的平凡扩张Trivial Extensions of G-graded Categories over k
曾灿波;陈清华;
摘要(Abstract):
设G为群,X为k上G-分次范畴.在定义C上k-函子F的基础上,证明了平凡扩张范畴C∝F仍为k上G-分次范畴;当F为X上分次k-函子时,给出了一族范畴同构,即r∈N(G),有(C#G)∝(F#r)(C∝F)r#G.
关键词(KeyWords): G-分次范畴;平凡扩张;分次k-函子
基金项目(Foundation): 国家自然科学基金资助项目(1037110110671161);; 福建省自然科学基金资助项目(Z0511022);; 福建省教育厅基金资助项目(JB04215JA050206JA06008)
作者(Authors): 曾灿波;陈清华;
参考文献(References):
- [1]Robert M Fossum,Phillip A Griffith,Idun Reiten.Trivial extensions of abelian categories[M].Berlin-Heidelberg-NewYork:Springer-Verlag,1975.
- [2]Claude Cibils,Eduardo N Marcos.Skew category,galois covering and smash product of a k-category[J].ProcAmer Math Soc,2006,134:39-50.
- [3]Xu Fei,Representations of categories and their applications[D].School of Mathematics,University of Minnesota,2006.
- [4]Nastasescus C,Oystaeyen F Van.Methods of graded rings[M].Berlin-Heidelberg-NewYork:Springer-Verlag,2004.
- [5]Frank W,Anderson Kent R Fuller.Rings and categories of modules(2nd edition)[M].New York:Spring-Verlag,1992.
- [6]Cohen M,Montgomery S.Group-graded rings,smash products and group actions[J].Trans Amer Math Soc,1984,282:237-258.
- [7]Ringel C M.Tame algebras and integral quadratic forms[M].New York:Springer-Verlag,1984.