共查询到20条相似文献,搜索用时 0 毫秒
1.
该文主要考虑了拟三角Hopf代数的某种Ore -扩张问题. 对拟三角Hopf代数的Ore -扩张何时保持相同的拟三角结构给出了充分必要条件. 最后作为应用, 文章讨论了Sweedler Hopf代数和Lusztig小量子群的Ore -扩张结构. 相似文献
2.
We characterize linear differential equations defined over a real differential field with a real closed field of constants C, which are solvable by real Liouville functions, as those having a differential Galois group whose identity component is solvable and C-split. 相似文献
3.
本文的目的 是定义Hopf二重Ore扩张,讨论这种扩张的基本性质并研究Hopf代数的分次与Hopf二重Ore扩张之间的关系.作者还研究了连通分次Hopf代数的结构及其Hopf二重Ore扩张的同调性质. 相似文献
5.
This article is devoted to faithfully flat Hopf bi-Galois extensions defined by Fischman, Montgomery, and Schneider. Let H be a Hopf algebra with bijective antipode. Given a faithfully flat right H-Galois extension A/ R and a right H-comodule subalgebra C ? A such that A is faithfully flat over C, we provide necessary and sufficient conditions for the existence of a Hopf algebra W so that A/ C is a left W-Galois extension and A a ( W, H)-bicomodule algebra. As a consequence, we prove that if R = k, there is a Hopf algebra W such that A/ C is a left W-Galois extension and A a ( W, H)-bicomodule algebra if and only if C is an H-submodule of A with respect to the Miyashita–Ulbrich action. 相似文献
6.
We characterize Galois extensions of Boolean algebras as finite extensions with the independent set of generators, answering a question of D. Monk. 相似文献
8.
There are considered trivial extensions of minimal 2-fundamental algebras. It is shown that if the Auslander–Reiten quiver Γ A of a minimal 2-fundamental algebra A contains a starting component or an ending component which is not generalized standard, then the Auslander–Reiten quiver Γ T(A) of the trivial extension T( A) of A contains also a component that is not a generalized standard. 相似文献
10.
The goal of this article is to generalize the theory of Hopf–Ore extensions on Hopf algebras to multiplier Hopf algebras. First the concept of a Hopf–Ore extension of a multiplier Hopf algebra is introduced. We give a necessary and sufficient condition for Ore extensions to become a multiplier Hopf algebra. Finally, *-structures are constructed on Hopf–Ore extensions, and certain isomorphisms between Hopf–Ore extensions are discussed. 相似文献
11.
Let H be a cosemisimple Hopf algebra over a field k, and π : A→ H be a surjective cocentral bialgebra homomorphism of bialgebras. The authors prove that if A is Galois over its coinvariants B=LH Ker π and B is a sub-Hopf algebra of A, then A is itself a Hopf algebra. This generalizes a result of Cegarra [3] on group-graded algebras. 相似文献
12.
Let H be a finite-dimensional Hopf algebra and A a finite-dimensional H-simple left H-module algebra. We show that the smash product A# H is isomorphic to End A′( V ? H*), where V ≠ 0 is a finite-dimensional left A-module and ( A′, V′) the stabilizer of ( A, V). As an application it is proved that A# H is isomorphic to a full matrix algebra over A′ when H is semisimple and dim V|dim A. 相似文献
13.
This note presents some results on projective modules and the Grothendieck groups K 0 and G 0 for Frobenius algebras and for certain Hopf Galois extensions. Our principal technical tools are the Higman trace for Frobenius algebras and a product formula for Hattori-Stallings ranks of projectives over Hopf Galois extensions. 相似文献
14.
The authors present the general theory of cleft extensions for a cocommutative weak Hopf algebra H.For a right H-comodule algebra,they obtain a bijective correspondence between the isomorphisms classes of H-cleft extensions AH → A,where AH is the subalgebra of coinvariants,and the equivalence classes of crossed systems for H over AH.Finally,they establish a bijection between the set of equivalence classes of crossed systems with a fixed weak H-module algebra structure and the second cohomology group HφZ(AH)2(H,Z(AH)),where Z(AH)is the center of AH. 相似文献
15.
Let , be finite-dimensional Lie algebras over a field of characteristic zero. Regard and , the dual Lie coalgebra of , as Lie bialgebras with zero cobracket and zero bracket, respectively. Suppose that a matched pair of Lie bialgebras is given, which has structure maps . Then it induces a matched pair of Hopf algebras, where is the universal envelope of and is the Hopf dual of . We show that the group of cleft Hopf algebra extensions associated with is naturally isomorphic to the group of Lie bialgebra extensions associated with . An exact sequence involving either of these groups is obtained, which is a variation of the exact sequence due to G.I. Kac. If , there follows a bijection between the set of all cleft Hopf algebra extensions of by and the set of all Lie bialgebra extensions of by . 相似文献
16.
Let H be a semisimple Hopf algebra over a field of characteristic 0, and A a finite-dimensional transitive H-module algebra with a l-dimensional ideal. It is proved that the smash product A#H is isomorphic to a full matrix algebra over some right coideal subalgebra N of H. The correspondence between A and such N, and the special case A = k(X) of function algebra on a finite set X are considered. 相似文献
18.
In this paper, the classical Galois theory to the H*-Galois case is developed. Let H be a semisimple and cosemisimple Hopf algebra over a field k, A a left H-module algebra,and A/AHa right H*-Galois extension. The authors prove that, if AHis a separable kalgebra, then for any right coideal subalgebra B of H, the B-invariants A~B= {a ∈ A |b · a = ε(b)a, b∈ B} is a separable k-algebra. They also establish a Galois connection between right coideal subalgebras of H and separable subalgebras of A containing AHas in the classical case. The results are applied to the case H =(kG)*for a finite group G to get a Galois 1-1 correspondence. 相似文献
19.
We construct the endofunctor 𝔲𝔠𝔢 between the category of Leibniz algebras which assigns to a perfect Leibniz algebra its universal central extension, and we obtain the isomorphism 𝔲𝔠𝔢 Lie(𝔮 Lie) ? (𝔲𝔠𝔢 Leib(𝔮)) Lie, where 𝔮 is a perfect Leibniz algebra satisfying the condition [ x, [ x, y]] + [[ x, y], x] = 0, for all x, y ∈ 𝔮. Moreover, we obtain several results concerning the lifting of automorphisms and derivations in a covering. We also study the relationship between the universal central extension of a semidirect product of perfect Leibniz algebras and the semidirect product of the universal central extension of both of them. 相似文献
|