共查询到20条相似文献,搜索用时 15 毫秒
1.
For a quasi-Hopf algebra H, an H-bicomodule algebra and an H-bimodule coalgebra C we will show that the category of two-sided two-cosided Hopf modules is equivalent to the category of right–left generalized Yetter–Drinfeld modules . Using alternative versions of this result we will recover the category isomorphism between the categories of left–left and
left–right Yetter–Drinfeld modules over a quasi-Hopf algebra.
相似文献
2.
L. Delvaux 《代数通讯》2013,41(8):2872-2882
We give a representation-theoretic and a categorical interpretation of the Drinfel'd double into the framework of group-cograded multiplier Hopf algebras. The Drinfel'd double as constructed by Zunino for a finite-type Hopf group-coalgebra is an example of this construction in the sense that the components of the group-cograded multiplier Hopf algebras are unital and finite-dimensional algebras and the admissible action is related with the adjoint action of the group on itself. 相似文献
3.
Jos Nicanor ALONSO LVAREZ Ramón GONZLEZ RODRIGUEZ Carlos SONEIRA CALVO 《数学学报(英文版)》2014,30(4):567-590
In this paper,we introduce several centralizer constructions in a monoidal context and establish a monoidal equivalence with the category of Yetter–Drinfeld modules over a weak braided Hopf monoid.We apply the general result to the calculus of the center in module categories. 相似文献
4.
5.
《代数通讯》2013,41(9):3403-3415
Abstract This paper, mainly gives a Fundamental Theorem of weak Doi–Hopf modules, which is not only generalizes the Fundamental Theorem of weak Hopf modules but also generalizes the Fundamental Theorem of relative Hopf modules. Moreover, it gives a sufficient and necessary condition for weak smash product algebras to be weak bialgebras, and a sufficient condition for weak smash product algebras to be semisimple weak Hopf algebras. 相似文献
6.
M. Beattie S. Dăscălescu ş. Raianu F. Van Oystaeyen 《Applied Categorical Structures》1998,6(2):223-237
We show that the two-sided two-cosided Hopf modules are in some case generalized Hopf modules in the sense of Doi. Then the equivalence between two-sided two-cosided Hopf modules and Yetter—Drinfeld modules, proved in [8], becomes an equivalence between categories of Doi—Hopf modules. This equivalence induces equivalences between the underlying categories of (co)modules. We study the relation between this equivalence and the one given by the induced functor. 相似文献
7.
We study Doi–Hopf data and Doi–Hopf modules for Hopf group-coalgebras. We introduce modules graded by a discrete Doi–Hopf datum; to a Doi–Hopf datum over a Hopf group coalgebra, we associate an algebra graded by the underlying discrete Doi–Hopf datum, using a smash product type construction. The category of Doi–Hopf modules is then isomorphic to the category of graded modules over this algebra. This is applied to the category of Yetter–Drinfeld modules over a Hopf group coalgebra, leading to the construction of the Drinfeld double. It is shown that this Drinfeld double is a quasitriangular ${\mathbb{G}}$ -graded Hopf algebra. 相似文献
8.
Bodo Pareigis 《Applied Categorical Structures》1998,6(2):151-175
The category of Yetter—Drinfeld modules
over a Hopf algebra K (with bijective antipode over a field k) is a braided monoidal category. If H is a Hopf algebra in this category then the primitive elements of H do not form an ordinary Lie algebra anymore. We introduce the notion of a (generalized) Lie algebra in
such that the set of primitive elements P(H) is a Lie algebra in this sense. Also the Yetter—Drinfeld module of derivations of an algebra A in
is a Lie algebra. Furthermore for each Lie algebra in
there is a universal enveloping algebra which turns out to be a Hopf algebra in
. 相似文献
9.
10.
To any right comodule coalgebra C over a Hopf algebra H we associate a left H-comodule algebra A. Under certain conditions, in particular in the case where H has nonzero integrals, we show that the category of right C, H-comodules is isomorphic to a certain subcategory of the category of Doi–Hopf modules associated to A. As an application, we investigate the connection between C and the smash coproduct C ? H being right semiperfect. 相似文献
11.
Let k be an algebraically closed field of characteristic zero, and D
n
be the dihedral group of order 2n, where n is a positive even integer. In this paper, we investigate Yetter-Drinfeld modules over the Hopf-Ore extension A(n, 0) of kD
n
. We describe the structures and properties of simple Yetter-Drinfeld modules over A(n, 0), and classify all simple Yetter-Drinfeld modules over A(n, 0). 相似文献
12.
Let (R∨,R) be a dual pair of Hopf algebras in the category of Yetter–Drinfeld modules over a Hopf algebra H with bijective antipode. We show that there is a braided monoidal isomorphism between rational left Yetter–Drinfeld modules over the bosonizations of R and of R∨, respectively. As an application of this very general category isomorphism we obtain a natural proof of the existence of reflections of Nichols algebras of semi-simple Yetter–Drinfeld modules over H. 相似文献
13.
14.
We prove a version of the Frobenius–Schur theorem for a finite-dimensional semisimple Hopf algebra H over an algebraically closed field; if the field has characteristic p not 0, H is also assumed to be cosemisimple. Then for each irreducible representation V of H, we define a Schur indicator for V, which reduces to the classical Schur indicator when H is the group algebra of a finite group. We prove that this indicator is 0 if and only if V is not self-dual. If V is self dual, then the indicator is positive (respectively, negative) if and only if V admits a nondegenerate bilinear symmetric (resp., skew-symmetric) H-invariant form. A more general result is proved for algebras with involution. 相似文献
15.
Hom-structures (Lie algebras, algebras, coalgebras, Hopf algebras) have been investigated in the literature recently. We study Hom-structures from the point of view of monoidal categories; in particular, we introduce a symmetric monoidal category such that Hom-algebras coincide with algebras in this monoidal category, and similar properties for coalgebras, Hopf algebras, and Lie algebras. 相似文献
16.
In this article we extend the Miyashita–Ulbrich action for weak H-Galois extensions associated to a weak bialgebra H. Also, if H is a weak Hopf algebra, we prove that this action induces a monoidal connection with the category of right-right Yetter–Drinfeld modules over H. 相似文献
17.
《Journal of Algebra》2002,247(2):467-508
In this paper we shall generalize the notion of an integral on a Hopf algebra introduced by Sweedler, by defining the more general concept of an integral of a threetuple (H, A, C), where H is a Hopf algebra coacting on an algebra A and acting on a coalgebra C. We prove that there exists a total integral γ: C → Hom(C, A) of (H, A, C) if and only if any representation of (H, A, C) is injective in a functorial way, as a corepresentation of C. In particular, the quantum integrals associated to Yetter–Drinfel'd modules are defined. Let now A be an H-bicomodule algebra, HA the category of quantum Yetter–Drinfel'd modules, and B = {a ∈ A|∑S− 1(a〈1〉)a〈 − 1〉 ⊗ a〈0〉 = 1H ⊗ a}, the subalgebra of coinvariants of the Verma structure A ∈ HA. We shall prove the following affineness criterion: if there exists γ: H → Hom(H, A) a total quantum integral and the canonical map β: A ⊗ B A → H ⊗ A, β(a ⊗ B b) = ∑S− 1(b〈1〉)b〈 − 1〉 ⊗ ab〈0〉 is surjective (i.e., A/B is a quantum homogeneous space), then the induction functor – ⊗ B A: B → HA is an equivalence of categories. The affineness criteria proven by Cline, Parshall, and Scott, and independently by Oberst (for affine algebraic groups schemes) and Schneider (in the noncommutative case), are recovered as special cases. 相似文献
18.
Applied Categorical Structures - Let $$H_1$$ and $$H_2$$ be Hopf algebras which are not necessarily finite dimensional and $$\alpha ,\beta \in Aut_{Hopf}(H_1),\gamma ,\delta \in Aut_{Hopf}(H_2)$$ .... 相似文献
19.
Kuei-Nuan Lin 《代数通讯》2013,41(9):3673-3682
Abstract The notion of quasi-polynomials is very important in the theory of functional identities. For example, results on quasi-polynomials were tools in the solution of long-standing Herstein's Lie map conjectures. In this paper, we show that functional identities involving quasi-polynomial of degree one have only standard solutions on d-free sets. 相似文献
20.
A Yetter—Drinfeld category over a Hopf algebra H with a bijective antipode, is equipped with a braiding which may be symmetric for some of its subcategories (e.g. when H is a triangular Hopf algebra). We prove that under an additional condition (which we term the u-condition) such symmetric subcategories completely resemble the category of vector spaces over a field k, with the ordinary flip map. Consequently, when Char k=0, one can define well behaving exterior algebras and non-commutative determinant functions. 相似文献