In this paper, we consider the graded path category associated to a quiver. We investigate all n-differentials on such a category, and also study the associated graded Lie algebra. Moreover, a necessary and sufficient...In this paper, we consider the graded path category associated to a quiver. We investigate all n-differentials on such a category, and also study the associated graded Lie algebra. Moreover, a necessary and sufficient condition is given for the graded path categorv to admit a DG category structure.展开更多
基金Project supported by the NationM Natural Science Foundation of China （No. 11271318, No. 11171296, No. J1210038）, the Specialized Research Fund for the Doctoral Program of Higher Education of China （No. 20110101110010） and the Zhejiang Provincial Natural Science Foundation of China （No. LZ13A010001 and No. J20100343）.Acknowledgements. The authors would like to thank the editor and referees for important suggestions and remarks. Also, the first author would like to thank Dr. Rongxiang Tian from Zhejiang University for her kind help in the process of this research.
文摘In this paper, we consider the graded path category associated to a quiver. We investigate all n-differentials on such a category, and also study the associated graded Lie algebra. Moreover, a necessary and sufficient condition is given for the graded path categorv to admit a DG category structure.
