In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod pow...In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod powers on product of two generators. Finally an algorithm was given to obtain these matrices.展开更多
The Leibniz-Hopf algebra is the free associative Z - algebra with one generator in each positive degree and coproduct is given by the Cartan formula. It has been also known as the ＇ring ofnoncommutative symmetric fun...The Leibniz-Hopf algebra is the free associative Z - algebra with one generator in each positive degree and coproduct is given by the Cartan formula. It has been also known as the ＇ring ofnoncommutative symmetric functions＇ [1], and to be isomorphic to the Solomon Descent algebra [ 12]. This Hopf algebra has links with algebra,topology and combinatorics. In this article we consider another approach of proof for the antipode formula in the Leibniz-Hopf algebra by using some properties of words in [2].展开更多
In this paper we prove that for a fixed l, the number of multiplicative ψ_k-module M=Z/p[y_1,…,y_1]/(Z/p[y_1,…,y_1])^(p+1)with degy_i=2b_i, i=1,…, l, is finite, and for a fixed l, the unstable polynomial A_p-al-ge...In this paper we prove that for a fixed l, the number of multiplicative ψ_k-module M=Z/p[y_1,…,y_1]/(Z/p[y_1,…,y_1])^(p+1)with degy_i=2b_i, i=1,…, l, is finite, and for a fixed l, the unstable polynomial A_p-al-gebras P(B)=Z/p[x_1,…,x_1] which are realizable are finite.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
We prove the so-called Unitary Hyperbolicity Theorem,a result on hyperbolicity of unitary involutions.The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the...We prove the so-called Unitary Hyperbolicity Theorem,a result on hyperbolicity of unitary involutions.The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the unitary one.While the original proofs in the orthogonal and symplectic cases were based on the incompressibility of generalized Severi-Brauer varieties,the proof in the unitary case is based on the incompressibility of their Weil transfers.展开更多
Let A be the mod p Steenrod algebra and S be the sphere spectrum localized at an odd prime p. To determine the stable homotopy groups of spheres π＊S is one of the central problems in homotopy theory. This paper cons...Let A be the mod p Steenrod algebra and S be the sphere spectrum localized at an odd prime p. To determine the stable homotopy groups of spheres π＊S is one of the central problems in homotopy theory. This paper constructs a new nontrivial family of homotopy elements in the stable homotopy groups of spheres πp^nq＋2pq＋q-3S which isof order p and is represented by kohn ∈ ExtA^3,P^nq＋2pq＋q（Zp,Zp） in the Adams spectral sequence, wherep 〉 5 is an odd prime, n ≥3 and q = 2（p-1）. In the course of the proof, a new family of homotopy elements in πp^nq＋（p＋1）q-1V（1） which is represented by β＊i＇＊i＊（hn） ∈ ExtA^2,pnq＋（p＋1）q＋1 （H^＊V（1）, Zp） in the Adams sequence is detected.展开更多
文摘In this study, particular matrices which is called P-matrices were defined for the action of the Steenrod powers on the polynomial algebra and it was shown that they can be used to calculate the action of Steenrod powers on product of two generators. Finally an algorithm was given to obtain these matrices.
文摘The Leibniz-Hopf algebra is the free associative Z - algebra with one generator in each positive degree and coproduct is given by the Cartan formula. It has been also known as the ＇ring ofnoncommutative symmetric functions＇ [1], and to be isomorphic to the Solomon Descent algebra [ 12]. This Hopf algebra has links with algebra,topology and combinatorics. In this article we consider another approach of proof for the antipode formula in the Leibniz-Hopf algebra by using some properties of words in [2].
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper we prove that for a fixed l, the number of multiplicative ψ_k-module M=Z/p[y_1,…,y_1]/(Z/p[y_1,…,y_1])^(p+1)with degy_i=2b_i, i=1,…, l, is finite, and for a fixed l, the unstable polynomial A_p-al-gebras P(B)=Z/p[x_1,…,x_1] which are realizable are finite.
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.
文摘We prove the so-called Unitary Hyperbolicity Theorem,a result on hyperbolicity of unitary involutions.The analogous previously known results for the orthogonal and symplectic involutions are formal consequences of the unitary one.While the original proofs in the orthogonal and symplectic cases were based on the incompressibility of generalized Severi-Brauer varieties,the proof in the unitary case is based on the incompressibility of their Weil transfers.
基金the National Natural Science Foundation of China(Nos.10501045,10771105)the Fund of the Personnel Division of Nankai University(No.J02017).
文摘Let A be the mod p Steenrod algebra and S be the sphere spectrum localized at an odd prime p. To determine the stable homotopy groups of spheres π＊S is one of the central problems in homotopy theory. This paper constructs a new nontrivial family of homotopy elements in the stable homotopy groups of spheres πp^nq＋2pq＋q-3S which isof order p and is represented by kohn ∈ ExtA^3,P^nq＋2pq＋q（Zp,Zp） in the Adams spectral sequence, wherep 〉 5 is an odd prime, n ≥3 and q = 2（p-1）. In the course of the proof, a new family of homotopy elements in πp^nq＋（p＋1）q-1V（1） which is represented by β＊i＇＊i＊（hn） ∈ ExtA^2,pnq＋（p＋1）q＋1 （H^＊V（1）, Zp） in the Adams sequence is detected.
