The classification of finite-dimensional pointed Hopf algebras with group S3 was finished in [AHS]: there are exactly two of them, the bosonization of a Nichols algebra of dimension 12 and a non-trivial lifting. Here we determine all simple modules over any of these Hopf algebras. We also find the Gabriel quivers, the projective covers of the simple modules, and prove that they are not of finit...

Let H be a finite-dimensional semisimple Hopf algebra. Recently it was shown in [LM] that a version of the Frobenius-Schur theorem holds for Hopf algebras, and thus that the Schur indicator ν(χ) of the character χ of a simple H-module is well-defined; this fact for the special case of Kac algebras was shown in [FGSV]. In this paper we show that for an important class of non-trivial Hopf algebra...

Abstract. We introduce analogs of the Hopf algebra of Free quasi-symmetric functions with bases labelled by colored permutations. When the color set is a semigroup, an internal product can be introduced. This leads to the construction of generalized descent algebras associated with wreath products Γ ≀ Sn and to the corresponding generalizations of quasi-symmetric functions. The associated Hopf ...

We give a pedagogical introduction to integration techniques appropriate for non-commutative spaces while presenting some new results as well. A rather detailed discussion outlines the motivation for adopting the Hopf algebra language. We then present some trace formulas for the integral on Hopf algebras and show how to treat the ∫ 1 = 0 case. We extend the discussion to braided Hopf algebras r...

Let H be a Hopf algebra over a field k and A a right coideal subalgebra of H , that is, A is a subalgebra satisfying ∆(A) ⊂ A⊗H where ∆ is the comultiplication in H . In case when H is finitely generated commutative, the right coideal subalgebras are intimately related to the homogeneous spaces for the corresponding group scheme. The purpose of this paper is to extend the class of pairsA,H for ...

For G a finite abelian group, we study the properties of general equivalence relations on Gn = Gn Sn , the wreath product of G with the symmetric group Sn , also known as the G-coloured symmetric group. We show that under certain conditions, some equivalence relations give rise to subalgebras of kGn as well as graded connected Hopf subalgebras of ⊕ n≥o kGn . In particular we construct a G-colou...

Bergeron and Li have introduced a set of axioms which guarantee that the Grothendieck groups of a tower of algebras L n≥0 An can be endowed with the structure of graded dual Hopf algebras. Hivert and Nzeutzhap, and independently Lam and Shimozono constructed dual graded graphs from primitive elements in Hopf algebras. In this paper we apply the composition of these constructions to towers of al...

Arithmetic root systems are invariants of Nichols algebras of diagonal type with a certain finiteness property. They can also be considered as generalizations of ordinary root systems with rich structure and many new examples. On the other hand, Nichols algebras are fundamental objects in the construction of quantized enveloping algebras, in the noncommutative differential geometry of quantum g...

1.1. Articole publicate in reviste cotate ISI. [1] A.L. Agore, G. Militaru, Unified products for Leibniz algebras. Applications, 25 pagini, Linear Algebra and its Applications, DOI: 10.1016/j.laa.2013.07.021. (IF 2012: 0,968; AIS 2012: 0,582) [2] A.L. Agore, G. Militaru, Extending structures for Lie algebras, 24 pagini, Monatshefte für Mathematik, DOI: 10.1007/s00605-013-0537-7. (IF 2012: 0,698...