共查询到20条相似文献,搜索用时 31 毫秒
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Let H be a weak Hopf algebra, A a right weak H-comodule algebra, and B the subalgebra of the H-coinvariant elements of A. Let A/B be a right weak H-Galois extension. In this paper, a spectral sequence for Ext which yields an estimate for the global dimension of A in terms of the corresponding data for H and B is constructed. Next, the relationship between the finitely presented dimensions of A and its subalgebra B are given. Further, the case in which A is an n-Gorenstein algebra is studied. 相似文献
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Xiao-Yan Zhou 《Acta Mathematica Hungarica》2013,138(1-2):140-146
Let H be a weak Hopf algebra, A a right weak H-comodule algebra and B the subalgebra of the H-coinvariant elements of?A. Let A/B be a right weak H-Galois extension. We prove that A/B is a separable extension if H is semisimple. Using this, we show that the global dimension and weak dimension of A are less than those of?B. As an application, we obtain Maschke-type theorems for weak Hopf?CGalois extensions and weak smash products. 相似文献
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Maschke-type theorem and Morita context over weak Hopf algebras 总被引:8,自引:0,他引:8
ZHANG Liangyun College of Science Nanjing Agricultural University Nanjing China Department of Mathematics Nanjing University Nanjing China 《中国科学A辑(英文版)》2006,49(5):587-598
This paper gives a Maschke-type theorem over semisimple weak Hopf algebras, extends the well-known Maschke-type theorem given by Cohen and Fishman and constructs a Morita context over weak Hopf algebras. 相似文献
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Byung-Jay Kahng 《代数通讯》2018,46(1):1-27
The Larson–Sweedler theorem says that a finite-dimensional bialgebra with a faithful integral is a Hopf algebra [15]. The result has been generalized to finite-dimensional weak Hopf algebras by Vecsernyés [44]. In this paper, we show that the result is still true for weak multiplier Hopf algebras. The notion of a weak multiplier bialgebra was introduced by Böhm et al. in [4]. In this note it is shown that a weak multiplier bialgebra with a regular and full coproduct is a regular weak multiplier Hopf algebra if there is a faithful set of integrals. Weak multiplier Hopf algebras are introduced and studied in [40]. Integrals on (regular) weak multiplier Hopf algebras are treated in [43]. This result is important for the development of the theory of locally compact quantum groupoids in the operator algebra setting, see [13] and [14]. Our treatment of this material is motivated by the prospect of such a theory. 相似文献
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CHEN Ju-zhen ZHANG Yan WANG Shuan-hong Dept.of Math. Southeast Univ. Nanjing China. 《高校应用数学学报(英文版)》2008,23(1):91-100
The main aim of this paper is to study the twisting theory of weak Hopf algebras and give an equivalence between the (braided) monoidal categories of weak Hopf bimodules over the original and the twisted weak Hopf algebra to generalize the result from Oeckl (2000). 相似文献
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We study certain aspects of the algebraic K-theory of Hopf–Galois extensions. We show that the Cartan map from K-theory to G-theory of such an extension is a rational isomorphism, provided the ring of coinvariants is regular, the Hopf algebra is finite dimensional and its Cartan map is injective in degree zero. This covers the case of a crossed product of a regular ring with a finite group and has an application to the study of Iwasawa modules. 相似文献
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Paul J. Truman 《代数通讯》2018,46(4):1420-1427
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设H是域k上任意的Hopf代数。本文首先讨论了右H_扩张A/A ̄(coH)与Hopf模范畴,给出了A/A ̄(coH)为右H-Galois扩张的充分必要条件和Hopf模范畴满足结构定理的若干等价条件.然后我们讨论了不可约作用与除环的Galois扩张. 相似文献
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Z. Wang 《Acta Mathematica Hungarica》2018,154(1):223-230
We generalize [4, Theorem 4.3] to the case of Hopf–Galois extension, by introducing the cotensor product of a comodule algebra and its opposite algebra, and then give some applications. 相似文献
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Shuan-hong Wang 《代数通讯》2013,41(2):521-546
Let G = NwrC n be the wreath product of N by C n , where N is a finite nilpotent group and C n is a cyclic group of order n. Then the normalizer property holds for G. 相似文献
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陈惠香 《数学年刊A辑(中文版)》1998,(3)
设Hopf代数H余作用于代数A.本文讨论代数A,余不变子代数AcoH及Smash积A#H的相互关系.同时将研究Hopf模,全积分及除环的HopfGalois扩张. 相似文献
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YIN Yanmin School of Mathematical Sciences Peking University Beijing China Department of Mathematics Shandong Institute of Architecture Engineering Jinan China 《中国科学A辑(英文版)》2005,48(7):958-971
We generalize the Morita theory to the Hopf algebroid and give the characterization of the surjectivity of one of the Morita context maps. 相似文献
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Tensor product decomposition rules for weight modules over the Hopf–Ore extensions of group algebras
In this paper, we investigate the tensor structure of the category of finite- dimensional weight modules over the Hopf–Ore extensions kG(χ?1,a,0) of group algebras kG. The tensor product decomposition rules for all indecomposable weight modules are explicitly given under the assumptions that k is an algebraically closed field of characteristic zero, and the orders of χ and χ(a) are the same. 相似文献
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The arrangement of all Galois lines for the Artin–Schreier–Mumford curve in the projective 3-space is described. Surprisingly, there exist infinitely many Galois lines intersecting this curve. 相似文献
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将Morita理论推广到Hopf代数胚上,并且研究了Morita关系中每一个映射的满射性质. 相似文献
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This paper gives a detailed analysis of the Cannon–Thurston maps associated to a general class of hyperbolic free group extensions. Let F denote a free group of finite rank at least 3 and consider a convex cocompact subgroup Γ ≤ Out(F), i.e. one for which the orbit map from Γ into the free factor complex of F is a quasi-isometric embedding. The subgroup Γ determines an extension EΓ of F, and the main theorem of Dowdall–Taylor [DT14] states that in this situation EΓ is hyperbolic if and only if Γ is purely atoroidal. 相似文献
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Yves Crama 《Mathematical Programming》1993,61(1-3):53-60
A well-known linearization technique for nonlinear 0–1 maximization problems can be viewed as extending any polynomial in 0–1 variables to a concave function defined on [0, 1]
n
. Some properties of this standard concave extension are investigated. Polynomials for which the standard extension coincides with the concave envelope are characterized in terms of integrality of a certain polyhedron or balancedness of a certain matrix. The standard extension is proved to be identical to another type of concave extension, defined as the lower envelope of a class of affine functions majorizing the given polynomial. 相似文献