Let p be an odd prime.The authors detect a nontrivial element p of order p^2 in the stable homotopy groups of spheres by the classical Adams spectral sequence.It is represented by a_0^(p-2)h_1 ∈ Ext_A^(p-1,pq+p-2)(...Let p be an odd prime.The authors detect a nontrivial element p of order p^2 in the stable homotopy groups of spheres by the classical Adams spectral sequence.It is represented by a_0^(p-2)h_1 ∈ Ext_A^(p-1,pq+p-2)(Z/p,Z/p) in the E_2-term of the ASS and meanwhile p · p is the first periodic element αp.展开更多
Let p be an odd prime and q = 2（p- 1）. Up to total degree t - s 〈 max（（5p^3 ＋ 6p^2 ＋6p ＋4）q- 10,p^4q}, the generators of H^s,t（U（L））, the cohomology of the universal enveloping algebra of a bigraded Lie a...Let p be an odd prime and q = 2（p- 1）. Up to total degree t - s 〈 max（（5p^3 ＋ 6p^2 ＋6p ＋4）q- 10,p^4q}, the generators of H^s,t（U（L））, the cohomology of the universal enveloping algebra of a bigraded Lie algebra L, are determined and their convergence is also verified. Furthermore our results reveal that this cohomology satisfies an analogous Poindare duality property. This largely generalizes an earlier classical results due to J. P. May.展开更多
基金supported by the National Natural Science Foundation of China(Nos.11761072,11671154)the China Postdoctoral Science Foundation Special Funded Project(No.2015T80909)
文摘Let p be an odd prime.The authors detect a nontrivial element p of order p^2 in the stable homotopy groups of spheres by the classical Adams spectral sequence.It is represented by a_0^(p-2)h_1 ∈ Ext_A^(p-1,pq+p-2)(Z/p,Z/p) in the E_2-term of the ASS and meanwhile p · p is the first periodic element αp.
基金supported by NSFC(Grant Nos.11671154 and 11761072)General Financial Grant from the China Postdoctoral Science Foundation(Grant No.2017M622721)
文摘Let p be an odd prime and q = 2（p- 1）. Up to total degree t - s 〈 max（（5p^3 ＋ 6p^2 ＋6p ＋4）q- 10,p^4q}, the generators of H^s,t（U（L））, the cohomology of the universal enveloping algebra of a bigraded Lie algebra L, are determined and their convergence is also verified. Furthermore our results reveal that this cohomology satisfies an analogous Poindare duality property. This largely generalizes an earlier classical results due to J. P. May.
