Fibonacci代数的Hochschild同调群The Hochschild homology groups of Fibonacci algebras
范金梅;
摘要(Abstract):
设Λd是Fibonacci代数,基于对Bardzell极小投射双模分解的细致分析,用组合的方法清晰地计算了Fibonacci代数Λd的各阶Hochschild同调群的维数.
关键词(KeyWords): Fibonacci代数;极小投射双模解;Hochschild同调群
基金项目(Foundation):
作者(Authors): 范金梅;
参考文献(References):
- [1]Hochschild G.On the cohomology groups of an associative algebra[J].Ann.Math.,1945,46:58-67.
- [2]Igusa K.Notes on the no loop conjecture[J].J.Pure Appl.Algebra,1990,69:161-176.
- [3]Han Y.Hochschild(co)homology dimension[EB/OL].Journal of the London Mathematical society,2006,73,http://d.wanfangdata.com.cn/NSTLQK NSTL QK11867631.aspx.
- [4]Avramov LL,Vigue′e-Poirrier M.Hochschild homology criteria for smoothness[J].Internat.Math.Research Notices,1992,1:17-25.
- [5]Happel D.Hochschild cohomology of finite-dimentional algebras[M].Berlin:Springer,1989.
- [6]Skowron′ski A.Simply connected algebras and Hochschild cohomology[J].Can.Math.Soc.Proc.,1993,14:431-447.
- [7]Gerstenhaber M.On the deformation of rings and algebras[J].Ann.Math.,1964,79:59-103.
- [8]徐运阁,曾祥勇.对偶扩张代数的Hochschild上同调群[J].数学学报,2006,49(1):59-68.
- [9]Zhang P.Hochschild cohomology of truncated basic cycle[J].Sci.China(Ser.A),1997,40:1272-1278.
- [10]Cibils C.Rigidity of truncated quiver algebras[J].Adv.Math.,1990,79:18-42.
- [11]Zhang P.The Hochschild homology of a truncated basic cycle[J].Algebra Colloq.,1998,5:77-84.
- [12]Liu S X,Zhang P.Hochschild homology of truncated algebras[J].Bull.London Math.Soc.,1994,26:427-430.
- [13]Cibils C.Rigid monomial algebras[J].Math.Ann.,1991,289:95-109.
- [14]Beilinson A,Ginzburg V,Soergel W.Koszul duality patterns in representaion theory[J].J.Amer.Math.Soc.,1996,9(2):473-527.
- [15]Green E L,Martinez-VillaR.Koszul and Yoneda algebras[J].Canad.Math.Soc.Conf.Proc.,1996,18:247-297.
- [16]Yu M I.Some remarks on Koszul algebras and quantum groups[J].Ann.Inst.Fourier(Grenoble),1987,37(4):191-205.
- [17]Parshall B J.Koszul algebras and duality[J].Canad.Math.Soc.Conf.Proc.,1995,16:277-285.
- [18]Green E L,Hartman G,Marcos EN,et al.Resolutions over Koszul algebras[J].Arch.Math.(Basel),2005,85:118-127.
- [19]Martinez-Villa R.Applications of Koszul algebras[J].Amer.Math.Soc.,1994,18:487-504.
- [20]Bardzell M J.The alternating syzygy behavior of monomial algebras[J].J.Algebra,1997,188:69-89.
- [21]Dlab V.Quasi-Hereditary Algebras[M].Appendix to Finite Dimensional Algebras by Drozd-.Kirichenko.Springer-Verlag,213-244.
- [22]范金梅,徐运阁.Fibonacci代数的Hochschild同调群[J].数学年刊:A辑,2007,28(3):359-370.
- [23]Bardzell M J.The alternating syzygy behavior of monomial algebras[J].J.Algebra,1997,188:69-89.