"Co-Frobenius" coalgebras were introduced as dualizations of Frobenius algebras. Recently, it was shown in \\cite{I} that they admit left-right symmetric characterizations analogue to those of Frobenius algebras: a coalgebra $C$ is co-Frobenius if and only if it is isomorphic to its ...
The antipode axioms have been changed by G. Böhm and K. Szlachányi (J. Algebra) in 2004 for tensor categorical reasons and to accommodate examples associated to depth two Frobenius algebra extensions.左Hopf代数体(H, R)是左双代数体和对映体：双代数体(H, R)由一个总代数H和一个基代数R...
algebra and bi—Frobenius algebra structure Chapter 3 The Stable Green Rings of Hopf Algebras 3.1 Stable Green rings 3.2 Bi—Frobenius algebra structure 3.3 Applications to Radford Hopf algebras Chapter 4 The Caslmlr Numbers of Green Rings 4.1 The Jacobson semisimplicity of Green rings 4.2 The ...
2.3Group-like algebra and bi-Frobenius algebra structure38 Chapter3The Stable Green Rings of Hopf Algebras43 3.1Stable Green rings43 3.2Bi-Frobenius algebra structure47 3.3Applications to Radford Hopf algebras49 Chapter4The Casimir Numbers of Green Rings55 ...
Define an FH-algebra H to be a Hopf algebra and a Frobenius algebra over R with a Frobenius homomorphism ψ such that ∑ ( h) h (1) ψ( h (2)) = ψ( h) · 1 for all h H. This is essentially the same as to co... B Pareigis - 《Journal of Algebra》 被引量: 27发表:...
Normal Basis and Transitivity of Crossed Products for Hopf Algebras (eng) Later, Hopf H-Galois extensions [19, 6] and Hopf subalgebras =-=[30, 38]-=- have been shown to be Frobenius extensions of the first and the ... HJ Schneider - 《Journal of Algebra》 被引量: 293发表: 1992年...
Motivated by this example we define the "Homology functor" (we prove it is homological) for any co-Frobenius algebra, with coefficients inH-comodules, that recover usual homology of a complex whenH=k[]#k[x]/x2. Another easy example of co-Frobenius Hopf algebra gives the category of "...
there is a weak Hopf algebraH with base A which is not Frobenius (and consequently, it is not Frobenius “over” A either).We give, moreover, a categorical counterpart of the result that a Hopf algebra is a Frobeniusalgebra for a noncoassociative generalization of weak Hopf algebra.1Introdu...
我们也建立 了双Frobenius模基本定理;得到了基本圈上双Frobenius代数的分类. 我们将双Frobenius代数置于辫子范畴中加以研究,得到了辫子双Frobe- nius模基本定理与辫子双Frobenius子代数存在的充分必要条件.从辫子Hopf 代数的观点出发我们研究了扭Hopf代数,特别地,利用Yetter—Drinfeld模构 造了一类有限维的扭Hopf代数,而...