On pointed Hopf algebras associated with unmixed conjugacy classes in Sm
نویسندگان
چکیده
منابع مشابه
ON POINTED HOPF ALGEBRAS ASSOCIATED TO SOME CONJUGACY CLASSES IN Sn NICOLÁS ANDRUSKIEWITSCH AND SHOUCHUAN ZHANG
We show that any pointed Hopf algebra with infinitesimal braiding associated to the conjugacy class of π ∈ Sn is infinitedimensional, if either the order of π is odd, or π is a product of disjoint cycles of odd order except for exactly two transpositions.
متن کاملON FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS ASSOCIATED TO SOME CONJUGACY CLASSES IN Sn NICOLÁS ANDRUSKIEWITSCH AND SHOUCHUAN ZHANG
We show that any pointed Hopf algebra with infinitesimal braiding associated to the conjugacy class of π ∈ Sn is infinitedimensional, if either the order of π is odd, or π is a product of disjoint cycles of odd order except for exactly two transpositions.
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In this paper, we study the duals of some finite dimensional pointed Hopf algebras working over an algebraically closed field k of characteristic 0. In particular, we study pointed Hopf algebras with coradical k[Γ] for Γ a finite abelian group, and with associated graded Hopf algebra of the form B(V )#k[Γ] where B(V ) is the Nichols algebra of V = ⊕iV χi gi ∈ k[Γ] k[Γ]YD. As a corollary to a ge...
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Definition 1.2 The invariants of H in A is the set A of those a ∈ A, that ha = ε(h)a for each h ∈ H. Straightforvard computations shows, that A is the subalgebra of A. We refer reader to [5], [6] for the basic information concerning Hopf algebras and their actions on associative algebras. As a generalization of the well-known fact for group actions the following question raised in [5] ( Questio...
متن کاملPointed Hopf Algebras with Abelian Coradical
In a previous work [AS2] we showed how to attach to a pointed Hopf algebra A with coradical kΓ, a braided strictly graded Hopf algebra R in the category Γ Γ YD of Yetter-Drinfeld modules over Γ. In this paper, we consider a further invariant of A, namely the subalgebra R of R generated by the space V of primitive elements. Algebras of this kind are known since the pioneering work of Nichols. It...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2007
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2436730