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1.
对偶余模函子()°和余反射余模 总被引:3,自引:0,他引:3
本文给出对偶余模M°的结构刻划及()°作为逆变函子的左正合性.同时引入余反射余模描述余反射余代数,由此研究余反射余代数的同调性质,证明当char(F)=0时,F[x1,...,xn]°上的Serre猜测是成立的,即F[x1,...,xn]°的有限余生成内射余模均为余自由的. 相似文献
2.
Smash积代数和量子模范畴中的Hopf代数的新对偶 总被引:4,自引:0,他引:4
本文引入模代数的一种新对偶,它推广了代数的有限对偶概念.并证明通过这种新对偶,模代数的对偶为余模余代数,从而形成Smash余积,而且证明了Smash积的对偶是Smash余积,即有(A#H)0≌HA0×H0余代数同构.最后证明量子模范畴中的Hopf代数通过这种新对偶是自对偶的. 相似文献
3.
本文引入模代数的一种新对偶,它推广了代数的有限对偶概念,并证明:通过这种新对偶,模代数的对偶为余模余代数,从而形成Smash余积,而且证明了Smash积的对偶是Smash余积,即有(A#H)~0 _HA~0×H~0余代数同构,最后证明量子模范畴中的Hopf代数通过这种新对偶是自对偶的。 相似文献
4.
5.
Hopf余模代数Smash积的理想陈惠香(扬州大学师范学院,扬州225002)本文恒设H是域k上Hopf代数,S为H的antipode,H“为H的对偶代数。如果S是双射,则用工表示S的逆映射.有关记号参阅文of].设A是右H一余模代数.则自然嵌人A①... 相似文献
6.
设 H是域 k上的有限维 Hopf代数,K为 H的任意子 Hopf代数,A是右 H-余模代数.设 =(H/K+ H)*和,且有 c∈A,t ·c=1.本 文刻划了 A作为 A# *-模的投射性且证明了:如果A/AH*是 H-Frobenius扩张, 则 A /AH*是 K-Frobenius扩张;如果 A/AH*是 H-Galois扩张,则 A */AH*是 K-Galois扩张. 相似文献
7.
设H是Hopf代数,A是右H-余模代数,若(,)满射,则J(A^coH)=L^H(A)∩^coH,而且,若J(A)是余模理想,则J(A^coH)=J^H(A)∩A^coH。 相似文献
8.
衡美芹 《纯粹数学与应用数学》2015,(3):273-281
主要讨论局部有限维的Hopfπ-代数H上π-模余代数与π-模余理想.给出了π-H-模余代数与π-H~*-余模代数之间的对偶关系,得到了π-H-模余理想的一个充分必要条件. 相似文献
9.
10.
赵士银 《纯粹数学与应用数学》2011,27(1):45-50
设H为有限型Hopfπ-代数,研究Hopfπ-代数H上的Hopfπ-模与Hopf π-余代数H *上的Hopfπ-余模之间的对偶关系,得出了Hopfπ-子模与Hopfπ-子 余模之间的充分必要条件,推广了Hopf代数中的相关结论. 相似文献
11.
We study certain comodule structures on spaces of linear morphisms between H-comodules, where H is a Hopf algebra over the field k. We apply the results to show that H has non-zero integrals if and only if there exists a non-zero finite dimensional injective right H-comodule. Using this approach, we prove an extension of a result of Sullivan, by showing that if H is involutory and has non-zero integrals, and there exists an injective indecomposable right comodule whose dimension is not a multiple of char(k), then H is cosemisimple. Also we prove without using character theory that if H is cosemisimple and M is an absolutely irreducible right H-comodule, then char(k) does not divide dim(M). 相似文献
12.
Alberto del Valle 《代数通讯》2013,41(4):1257-1269
The formula dim(A+B)=dim(A)+dim(B)-dim(A∩B) works when ‘dim’ stands for the dimension of subspaces A,B of any vector space. In general, however, it does no longer hold if 'dim' means the uniform (or Goldie) dimension of submodules A,B of a module M over a ring R, and in fact the left hand side may be infinite while the right hand side is finite. In this paper we shall give a characterization of those modules M in which the formula holds for any two submodules A,B, as well as some conditions in the ring R which guarantee that dim(A+B) is finite whenever A and B are finite dimensional R-modules. 相似文献
13.
Yasuji Takeuchi 《代数通讯》2013,41(5):1657-1664
Let C be a coalgebra and let M be a right C-comodule. In this article we investigate the dimension of the space f of comodule morphisms from C to M. Our main result (Theorem 4) states that dim(∫M)≤dim(M), for every left co-Frobeuius coalgebra (with some additional properties) and for every finite dimensional right comodule M. In particular, taking M = ki we obtain 相似文献
14.
V. E. Govorov 《Mathematical Notes》1973,14(3):789-792
Let algebra R = Λ/P, where Λ is a free algebra over a field w. gl. dim R: = {min n ¦? R-modules X, Y, Tor n+1 R (X, Y)=0}. In order that w. gl. dim R≤2n (w. gl. dim R≤2n+1), it is necessary and sufficient that, for any two ideals of algebra Λ, a left ideal A and a right ideal B, containing ideal P, the following equation holds: $$AP^n \cap P^n B = AP^n B + P^{n + 1} (AP^n B \cap P^{n + 1} = AP^{n + 1} + P^{n + 1} B).$$ 相似文献
15.
令M_1为一个有限的von Neumann代数,τ_1为其上的一个忠实正规迹态.我们将证明,如果M_1中存在一列两两正交的酉元列{u_k:k∈N},则对任意具有忠实正规迹态τ_2的有限von Neumann代数M_2(≠C),迹自由积(M_1,τ_1)*(M_2,τ_2)是Ⅱ_1型因子.作为推论可以得出,如果M_1有一个von Neumann子代数N不包含最小投影,则对任意具有忠实迹态τ_2的有限von Neumann代数M_2(≠C),迹自由积(M_1,τ_1)*(M_2,τ_2)是Ⅱ_1型因子. 相似文献
16.
Let ${\mathfrak{a}}$ be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. It is shown that ${{\rm Ann}_R(H_{\mathfrak{a}}^{{\rm dim} M}(M))= {\rm Ann}_R(M/T_R(\mathfrak{a}, M))}$ , where ${T_R(\mathfrak{a}, M)}$ is the largest submodule of M such that ${{\rm cd}(\mathfrak{a}, T_R(\mathfrak{a}, M)) < {\rm cd}(\mathfrak{a}, M)}$ . Several applications of this result are given. Among other things, it is shown that there exists an ideal ${\mathfrak{b}}$ of R such that ${{\rm Ann}_R(H_{\mathfrak{a}}^{{\rm dim} M}(M))={\rm Ann}_R(M/H_{\mathfrak{b}}^{0}(M))}$ . Using this, we show that if ${ H_{\mathfrak{a}}^{{\rm dim} R}(R)=0}$ , then ${{{\rm Att}_R} H^{{\rm dim} R-1}_{\mathfrak a}(R)= \{\mathfrak{p} \in {\rm Spec} R | \,{\rm cd}(\mathfrak{a}, R/\mathfrak{p}) = {\rm dim} R-1\}.}$ These generalize the main results of Bahmanpour et al. (see [2, Theorem 2.6]), Hellus (see [7, Theorem 2.3]), and Lynch (see [10, Theorem 2.4]). 相似文献
17.
Lin Jinkun 《数学年刊B辑(英文版)》1987,8(2):131-141
Let Q_i,P^R be Milnor base elements of the mod p Steenrod algebra, p>2. P_i^s=P^(0,\cdots0,p^s,0,\cdots) with p^s in the t-th position, s相似文献
18.
Let H be a Hopf algebra over a field k. Under some assumptions on H we state and prove a generalization of the Wedderburn-Malcev theorem for i7-comodule algebras. We show that our version of this theorem holds for a large enough class of Hopf algebras, such as coordinate rings of completely reducible affine algebraic groups, finite dimensional Hopf algebras over fields of characteristic 0 and group algebras. Some dual results are also included. 相似文献
19.
Paul-Jean Cahen 《manuscripta mathematica》1990,67(1):333-343
Let A be a commutative domain with quotient field K and AS the ring of integer-valued polynomials thus AS={f∈K[X]; f(A)⊂A}; we show that the Krull dimension of AS is such that dim AS≥dim A[X]-1 and give examples where dim AS=dim A[X]-1. Considering chains of primes of AS above a maximal idealm of finite residue field, we give also examples where the length of such a chain can arbitrarily be prescribed (whereas in
A[X] the length of such chains is always 1). To provide such examples we consider a pair of domains A⊂B sharing an ideal I
such that A/I is finite; we give sufficient conditients to have AS⊂B[X] and show that in this case dim AS=dim B[X]. At last, as a generalisation of Noetherian rings of dimension 1, we consider domains with an ideal I such that
A/I is finite and a power In of I is contained in a proper principal ideal of A; for such domains we show that every prime of AS above a primem containing I is maximal.
相似文献
20.
Peyman Niroomand 《Central European Journal of Mathematics》2011,9(1):57-64
Let L be an n-dimensional non-abelian nilpotent Lie algebra and $
s(L) = \frac{1}
{2}(n - 1)(n - 2) + 1 - \dim M(L)
$
s(L) = \frac{1}
{2}(n - 1)(n - 2) + 1 - \dim M(L)
where M(L) is the Schur multiplier of L. In [Niroomand P., Russo F., A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra (in press)] it has
been shown that s(L) ≥ 0 and the structure of all nilpotent Lie algebras has been determined when s(L) = 0. In the present paper, we will characterize all finite dimensional nilpotent Lie algebras with s(L) = 1; 2. 相似文献