A finitely generated projective Hopf algebra H over R has an antipode if and only if H is a Frobenius algebra with a Frobenius homomorphism ψ such that Σ h (1) ψ( h (2)) = ψ( h) · 1 for all h H. We also show that the antipode is bijective and that the ideal of left ...
Hopf algebraModular groupFrobenius algebra16Txx16B5018D10We discuss algebraic and representation theoretic structures in braided tensor categories C which obey certain finiteness conditions. Much interesting structure of such a category is encoded in a Hopf algebra H in C. In particular, the Hopf ...
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...
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 "...
A multiplier Hopf algebra is an algebra A with or without identity and a homomorphism Δ from A to the multiplier algebra of A ⊗ A satisfying certain axioms (such as a form of coassociativity). From: Handbook of Algebra, 2006 About this pageSet alert ...
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 ...
In this note we show that a finite dimensional, semisimple, lower solvable Hopf algebra is always of Frobenius type, in arbitrary characteristic.doi:10.1080/00927870701302198LetzterEdward S.EbscoCommunications in AlgebraE. Letzter, Commutator Hopf subalgebras and irreducible representations, preprint, ar...
Let (H, R) be a co-Frobenius quasitriangular Hopf algebra with antipode S. Denote the set of group-like elements in H by G (H). In this paper, we find a necessary and sufficient condition for (H, R) to have a ribbon element. The condition gives a connection with the order of G...
COMPUTINGTHEFROBENIUS-SCHURINDICATORFOR ABELIANEXTENSIONSOFHOPFALGEBRAS Y.KASHINA,G.MASON,ANDS.MONTGOMERY 1.Introduction LetHbeafinite-dimensionalsemisimpleHopfalgebra.Recentlyitwasshownin [LM]thataversionoftheFrobenius-SchurtheoremholdsforHopfalgebras,andthus thattheSchurindicatorν(χ)ofthecharacterχofasimple...
and coactions on associative algebras. Particular questions discussed are conditions ensuring that a Hopf module algebra is Frobenius or quasi-Frobenius, existence of classical quotient rings for Hopf module algebras, extension of the module structure to quotient rings, projectivity and faithful flatness...