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251.
Marino Gran Florence Sterck Joost Vercruysse 《Journal of Pure and Applied Algebra》2019,223(10):4171-4190
We prove that the category of cocommutative Hopf algebras over a field is a semi-abelian category. This result extends a previous special case of it, based on the Milnor–Moore theorem, where the field was assumed to have zero characteristic. Takeuchi's theorem asserting that the category of commutative and cocommutative Hopf algebras over a field is abelian immediately follows from this new observation. We also prove that the category of cocommutative Hopf algebras over a field is action representable. We make some new observations concerning the categorical commutator of normal Hopf subalgebras, and this leads to the proof that two definitions of crossed modules of cocommutative Hopf algebras are equivalent in this context. 相似文献
252.
Our main result is a proof of the Florent Hivert conjecture [F. Hivert, Local action of the symmetric group and generalizations of quasi-symmetric functions, in preparation] that the algebras of r-Quasi-Symmetric polynomials in x1,x2,…,xn are free modules over the ring of Symmetric polynomials. The proof rests on a theorem that reduces a wide variety of freeness results to the establishment of a single dimension bound. We are thus able to derive the Etingof-Ginzburg [P. Etingof, V. Ginzburg, On m-quasi-invariants of a Coxeter group, Mosc. Math. J. 2 (2002) 555-566] Theorem on m-Quasi-Invariants and our r-Quasi-Symmetric result as special cases of a single general principle. Another byproduct of the present treatment is a remarkably simple new proof of the freeness theorem for 1-Quasi-Symmetric polynomials given in [A.M. Garsia, N. Wallach, Qsym over Sym is free, J. Combin. Theory Ser. A 104 (2) (2003) 217-263]. 相似文献
253.
对定义在完备随机内积模的稠子模上的模同态引入了共轭算子的概念并讨论其基本性质,尤其证明了共轭算子的闭性. 相似文献
254.
Michel Dubois-violette 《K-Theory》1998,14(4):371-404
We study the generalized homology associated with a nilpotent endomorphism d satisfying d
N = 0,For simplicial modules, we construct such nilpotent endomorphisms and we prove a general result relating the corresponding generalized homologies to the ordinary homology. We also discuss the generalization of the notion of graded differential algebra in this context. 相似文献
255.
本文首先讨论了微分算子Lie代数的单性,然后确定出了微分算子Lie代数的权重数都是1的所有不可约Harish-Chandra模。 相似文献
256.
257.
Craig Huneke Graham J. Leuschke 《Proceedings of the American Mathematical Society》2003,131(10):3003-3007
We prove (the excellent case of) Schreyer's conjecture that a local ring with countable CM type has at most a one-dimensional singular locus. Furthermore, we prove that the localization of a Cohen-Macaulay local ring of countable CM type is again of countable CM type.
258.
广义FP—内射模、广义平坦模与某些环 总被引:2,自引:0,他引:2
左(右)R-模A称为GFP-内射模,如果ExtR(M,A)=0对任-2-表现R-模M成立;左(右)R-模称为G-平坦的,如果Tor1^R(M,A)=0(Tor1^R(AM)=0)对于任一2-表现右(左)R-模M成立;环R称左(右)R-半遗传环,如果投射左(右)R-模的有限表现子模是投射的,环R称为左(右)G-正而环,如果自由左(右)R-模的有限表现子模为其直和项,研究了GFP-内射模和G-平坦模的一些性质,给出了它们的一些等价刻划,并利用它们刻划了凝聚环,G-半遗传环和G-正则环。 相似文献
259.
对于可换环 R,本文通过引进 K0R;分别给出了三类模范畴的 K0群(K0R,K0R,K0R)的有关性质及特征,同时本文还讨论了它们三者之间的关系. 相似文献
260.
For an additive subgroup G of a field F of characteristic zero, a Lie algebra B(G) of Block type is defined with basis {Lα,i| α∈G, i∈Z+} and relations [Lα,i, Lβ,j] = (β-α)Lα+β,i+j+(αj-βi)Lα+β,Lα+β,i+j-1.It is proved that an irreducible highest weight B(Z)-module is quasifinite if and only if it is a proper quotient of a Verma module. Furthermore, for a total order λ on G and any ∧∈B(G)0^*(the dual space of B(G)0 = span{L0,i|i∈Z+}), a Verma B(G)-module M(∧,λ) is defined, and the irreducibility of M(A,λ) is completely determined. 相似文献