In this article, we explore in some detail the free and weakly projective objects of the variety of Łukasiewicz implication algebras (the implicative subreducts of MV-algebras). We review the two already known descriptions ...

We show that all unipotent classes in finite simple Chevalley or Steinberg groups, different from PSLn(q) and PSp2n(q), collapse (i.e. are never the support of a finite-dimensional Nichols algebra), with a possible exception ...

This is a contribution to the classification of finite-dimensional Hopf algebras over an algebraically closed field k of characteristic 0. Concretely, we show that a finite-dimensional Hopf algebra whose Hopf coradical is ...

We describe how to find quantum determinants and antipode formulas from braidedvector spaces using the FRT-construction and finite-dimensional Nichols algebras. It improvesthe construction of quantum function algebras using ...

In this paper we give an explicit description of the left adjoint of the forgetful functor from the algebraic category of Gödel algebras with successor to the algebraic category of bounded prelinear Hilbert algebras with ...

Consider any subvariety of BL-algebras generated by a single BL-chain which is the ordinal sum of the standard MV-algebra on [0,1] and a basic hoop H. We present a geometrical characterization of elements in the finitely ...

Let K be a field of characteristic zero, g be a finite dimensional K-Lie algebra and let A be a finite dimensional associative and commutative K-algebra with unit. We describe the structure of the Lie algebra of derivations ...

We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from PSLn(q) collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a ...

For n, m ∈ N, let Hn,m be the dual of the Radford algebra of dimension n 2m. We present new finite-dimensional Nichols algebras arising from the study of simple Yetter-Drinfeld modules over Hn,m. Along the way, we describe ...

We classify all finite-dimensional Hopf algebras over an algebraically closed field of characteristic zero such that its coradical is isomorphic to the algebra of functions k D m over a dihedral group D m , with m=4a≥12. ...