共查询到20条相似文献,搜索用时 15 毫秒
1.
Florin Panaite Freddy Van Oystaeyen 《Proceedings of the American Mathematical Society》2007,135(6):1669-1677
If is a quasi-Hopf algebra and is a right -comodule algebra such that there exists a morphism of right -comodule algebras, we prove that there exists a left -module algebra such that . The main difference when comparing to the Hopf case is that, from the multiplication of , which is associative, we have to obtain the multiplication of , which in general is not; for this we use a canonical projection arising from the fact that becomes a quasi-Hopf -bimodule.
2.
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
3.
With an aim of exploring homological algebra for weak Hopf modules, this paper investigates the HOM-functor and presents the structure theorem for endomorphism algebras of weak two-sided (A,H)-Hopf modules, and gives the duality theorem for weak “big” smash products. 相似文献
4.
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
5.
Serge Skryabin 《Transactions of the American Mathematical Society》2007,359(6):2597-2623
Let be a Hopf algebra and an -simple right -comodule algebra. It is shown that under certain hypotheses every -Hopf module is either projective or free as an -module and is either a quasi-Frobenius or a semisimple ring. As an application it is proved that every weakly finite (in particular, every finite dimensional) Hopf algebra is free both as a left and a right module over its finite dimensional right coideal subalgebras, and the latter are Frobenius algebras. Similar results are obtained for -simple -module algebras.
6.
G. C. Wraith 《Annali di Matematica Pura ed Applicata》1967,76(1):149-163
Summary In any category with products and a terminal object one may define the notions of group, module over a group etc. if f: R′→R
is a homomorphism of groups, and M an R-module, then one has an induced R′-module f*(M). If one is working in the category
of sets, one may define a functor left adjoint to f* by N→R⊗R′ N, where N is an R′-module. In this paper we show that f* has a left adjoint when one is working in the category of graded
connected coalgebras over a field. 相似文献
7.
Let 𝒜 be a commutative unital algebra over an algebraically closed field k of characteristic ≠2, whose generators form a finite-dimensional subspace V, with no nontrivial homogeneous quadratic relations. Let 𝒬 be a Hopf algebra that coacts on 𝒜 inner-faithfully, while leaving V invariant. We prove that 𝒬 must be commutative when either: (i) the coaction preserves a non-degenerate bilinear form on V; or (ii) 𝒬 is co-semisimple, finite-dimensional, and char(k) = 0. 相似文献
8.
V. A. Artamonov 《Journal of Mathematical Sciences》1994,71(2):2289-2328
This survey considers work published between 1970 and 1990 on the algebraic aspects of Hopf theory. There are detailed discussions of the properties of antipodes, group and primitive elements, integrals, crossed products, Galois theory, Lie coalgebras, the category of Hopf algebras, quantum groups, etc.Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 29, pp. 3–63, 1991. 相似文献
9.
《Journal of Pure and Applied Algebra》1987,47(3):243-252
An algebraic theory of bordism via characteristic numbers, analogous to topological bordism, is given. The Steenrod algebra is replaced by a fairly general graded Hopf algebra A, topological spaces by algebras over A, vector bundles by Thom modules, and closed manifolds by Poincaré algebras over A. 相似文献
10.
Zhi-xiang Wu 《高校应用数学学报(英文版)》2018,33(1):107-126
In this paper, we study a Yetter-Drinfeld module V over a weak Hopf algebra H.Although the category of all left H-modules is not a braided tensor category, we can define a Yetter-Drinfeld module. Using this Yetter-Drinfeld modules V, we construct Nichols algebra B(V) over the weak Hopf algebra H, and a series of weak Hopf algebras. Some results of [8] are generalized. 相似文献
11.
J. N. Alonso Álvarez J. M. Fernández Vilaboa R. González Rodríguez A. B. Rodríguez Raposo 《数学学报(英文版)》2008,24(12):2065-2080
In this paper, we give a necessary and sufficient condition for a comodule algebra over a weak Hopf algebra to have a total integral, thus extending the classical theory developed by Doi in the Hopf algebra setting. Also, from these results, we deduce a version of Maschke's Theorem for (H, B)-Hopf modules associated with a weak Hopf algebra H and a right H-comodule algebra B. 相似文献
12.
Phùng Hô Hai 《Israel Journal of Mathematics》2008,167(1):193-225
We show that a Hopf algebroid can be reconstructed from a monoidal functor from a monoidal category into the category of rigid
bimodules over a ring. We study the equivalence between the original category and the category of comodules over the reconstructed
Hopf algebroid. 相似文献
13.
Gabriella Böhm 《Annali dell'Universita di Ferrara》2005,51(1):233-262
An extensionB⊂A of algebras over a commutative ringk is anH-extension for anL-bialgebroidH ifA is anH-comodule algebra andB is the subalgebra of its coinvariants. It isH-Galois if the canonical mapA ⊗B
A →A ⊗L
H is an isomorphism or, equivalently, if the canonical coringA ⊗L
H:A is a Galois coring.
In the case of Hopf algebroid
anyH
R-extension is shown to be also anH
L-extension. If the antipode is bijective then also the notions ofH
R-Galois extensions and ofH
L-Galois extensions are proven to coincide.
Results about bijective entwining structures are extended to entwining structures over non-commutative algebras in order to
prove a Kreimer-Takeuchi type theorem for a finitely generated projective Hopf algebroidH with bijective antipode. It states that anyH-Galois extensionB⊂A is projective, and ifA isk-flat then already the surjectivity of the canonical map implies the Galois property.
The Morita theory, developed for corings by Caenepeel, Vercruysse and Wang is applied to obtain equivalent criteria for the
Galois property of Hopf algebroid extensions. This leads to Hopf algebroid analogues of results for Hopf algebra, extensions
by Doi and, in the case of Frobenius Hopf algebroids, by Cohen, Fishman and Montgomery.
Sunto Un'estensioneB(A di algebre su un anello commutativok è unaH-estensione per unL-bialgebroideH seA è unaH-comodulo algebra eB è la sottoalgebra dei suoi coinvarianti. Essa èH-Galois se l'applicazione canonicaA ⊗A B→A ⊗L H è un isomorfismo o, equivalentemente, se il coanello canonicoA ⊗L H:A è un coanello di Galois. Nel caso di un algebroide di Hopf si dimostra che ogniH R-estensione è unaH L-estensione. Se l'antipode è biiettivo allora si dimostra che anche le nozioni di estensioniH R-Galois eH L-Galois coincidono. I risultati per le strutture biiettive entwining sono estesi alle strutture entwining su algebre non commutative, al fine di dimostrare un teorema simile al Teorema dii Kreimer-Takeuchi per un Hopf algebroideH proiettivo finitamento generato con antipode biiettivo. Il teorema afferma che ogni estensioneH-GaloisB ⊂A è proiettiva e seA èk-piatto allora la suriettività dell'applicazione canonica è sufficiente a garantire la proprietà di Galois. La teoria di Morita, sviluppata per i coanelli da Caenepeel, Vercruysse e Wang, viene applicata per ottenere criteri equivalenti per la proprietà di Galois per estensioni di algebroidi di Hopf. Questo conduce a risultati analoghi, per algebroidi di Hopf, a quelli ottenuti da Doi per estensioni di algebre di Hopf e da Cohen Fishman e Montgomery nel caso degli algebroidi di Hopf Frobenius.相似文献
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15.
Akira Masuoka 《Proceedings of the American Mathematical Society》1996,124(3):735-737
We give an algebraic version of a result of G. I. Kac, showing that a semisimple Hopf algebra of dimension , where is a prime and , over an algebraically closed field of characteristic 0 contains a non-trivial central group-like. As an application we prove that, if , is isomorphic to a group algebra.
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For k a commutative ring, H a k‐bialgebra and A a right H‐comodule k‐algebra, we define a new multiplication on the H‐comodule A to obtain a twisted algebra” AT, T sumHom(H,End (A)). If T is convolution invertible, the categories of relative right Hopf modules over A and ATare isomorphic. Similarly a convolution invertible left twisting gives an isomorphism of the categories of relative left Hopf modules. We show that crossed products are invertible twistings of the tensor product, and obtain, as a corollary, a duality theorem for crossed products 相似文献
19.
Lars Kadison 《Proceedings of the American Mathematical Society》2003,131(10):2993-3002
Since an H-separable extension is of depth two, we associate to it dual bialgebroids and over the centralizer as in Kadison-Szlachányi. We show that has an antipode and is a Hopf algebroid. is also Hopf algebroid under the condition that the centralizer is an Azumaya algebra over the center of . For depth two extension , we show that .
20.
Martín Mombelli 《Mathematische Zeitschrift》2010,266(2):319-344
We develop some techniques for studying exact module categories over some families of pointed finite-dimensional Hopf algebras.
As an application we classify exact module categories over the tensor category of representations of the small quantum groups
uq(\mathfraksl2){u_q(\mathfrak{sl}_2)}. 相似文献