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We obtain the necessary and sufficient conditions for Radford’s biproduct to be a braided Hopf algebra. As an application, a nontrivial example is given. 相似文献
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The Yetter-Drinfeld category of the Hopf algebra over a field is a pre braided category. In this paper we prove this result for the weak Hopf algebra. We study the smash product and smash coproduct, weak biproducts in the weak Hopf algebra over a field k. For a weak Hopf algebra A in left Yetter-Drinfeld category HHYD. we prove that the weak biproducts of A and H is a weak Hopf algebra. 相似文献
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Tianshui Ma 《代数通讯》2013,41(9):3206-3242
In this article, we first introduce the notion of a bitwistor and discuss conditions under which such bitwistor forms a bialgebra as a generalization of the well-known Radford's biproduct. Then, in order to obtain new quasitriangular bialgebras, we consider a construction called twisted tensor biproduct, which is a special case of bitwistor bialgebra, and give a necessary and sufficient condition for such twisted tensor biproduct to admit quasitriangular structures. 相似文献
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Let(H, β) be a Hom-bialgebra such that β~2= id_H.(A, α_A) is a Hom-bialgebra in the left-left Hom-Yetter-Drinfeld category (_H~H)YD and(B, α_B) is a Hom-bialgebra in the right-right Hom-Yetter-Drinfeld category YD_H~H. The authors define the two-sided smash product Hom-algebra(A■H■B, α_A ? β ? α_B) and the two-sided smash coproduct Homcoalgebra(A◇H◇B, α_A ? β ? α_B). Then the necessary and sufficient conditions for(A■H■B, α_A ? β ? α_B) and(A◇H◇B, α_A ? β ? α_B) to be a Hom-bialgebra(called the double biproduct Hom-bialgebra and denoted by(A_◇~■H_◇~■B, α_A ? β ? α_B)) are derived. On the other hand, the necessary and sufficient conditions for the smash coproduct Hom-Hopf algebra(A◇H, α_A ? β) to be quasitriangular are given. 相似文献
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FERNNDEZ VILABOA Jose Manuel GONZLEZ RODRíGUEZ Ramon RODRíGUEZ RAPOSO Ana Belen 《中国科学 数学(英文版)》2012,55(7):1321-1352
In this paper, we present the general theory and universal properties of weak crossed biproducts. We prove that every weak projection of weak bialgebras induces one of these weak crossed structures. Finally, we compute explicitly the weak crossed biproduct associated with a groupoid that admits an exact factorization. 相似文献
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L. Delvaux 《Algebras and Representation Theory》2007,10(6):533-554
Let B be a regular multiplier Hopf algebra. Let A be an algebra with a non-degenerate multiplication such that A is a left B-module algebra and a left B-comodule algebra. By the use of the left action and the left coaction of B on A, we determine when a comultiplication on A makes A into a “B-admissible regular multiplier Hopf algebra.” If A is a B-admissible regular multiplier Hopf algebra, we prove that the smash product A # B is again a regular multiplier Hopf algebra. The comultiplication on A # B is a cotwisting (induced by the left coaction of B on A) of the given comultiplications on A and B. When we restrict to the framework of ordinary Hopf algebra theory, we recover Majid’s braided interpretation of Radford’s
biproduct.
Presented by K. Goodearl. 相似文献
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Sonia Natale 《Algebras and Representation Theory》2004,7(2):173-188
Let p and q be distinct prime numbers. We prove a result on the existence of nontrivial group-like elements in a certain class of semisimple Hopf algebras of dimension pq
r
. We conclude the classification of semisimple Hopf algebras A of dimension pq
2 over an algebraically closed field k of characteristic zero, such that both A and A
* are of Frobenius type. We also complete the classification of semisimple Hopf algebras of dimension pq
2<100. 相似文献
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