Hans Schneider, 1927–2015

Small Quantum Groups and the Classification of Pointed Hopf Algebras Nicolás Andruskiewitsch and Hans-jürgen Schneider

In this paper we apply the theory of the quantum groups Uq(g), and of the small quantum groups uq(g) for q a root of unity, g a semisimple complex Lie algebra, to obtain a classification result for an abstractly defined class of Hopf algebras. Since these Hopf algebras turn out to be deformations of a natural class of generalized small quantum groups, our result can be read as an axiomatic desc...

Finite Quantum Groups over Abelian Groups of Prime Exponent Nicolás Andruskiewitsch and Hans-jürgen Schneider

Since the discovery of quantum groups (Drinfeld, Jimbo) and finite dimensional variations thereof (Lusztig, Manin), these objects were studied from different points of view and had many applications. The present paper is part of a series where we intend to show that important classes of Hopf algebras are quantum groups and therefore belong to Lie theory. One of our main results is the explicit ...

ISOMORPHISM CLASSES AND AUTOMORPHISMS OF FINITE HOPF ALGEBRAS OF TYPE An NICOLÁS ANDRUSKIEWITSCH AND HANS-JÜRGEN SCHNEIDER

In [AS2] we classified a large class of finite-dimensional pointed Hopf algebras up to isomorphism. However the following problem was left open for Hopf algebras of of type A,D or E6, that is whose Cartan matrix is connected and allows a non-trivial automorphism of the corresponding Dynkin diagram. In this case we described the isomorphisms between two such Hopf algebras with the same Cartan ma...

THE NICHOLS ALGEBRA OF A SEMISIMPLE YETTER-DRINFELD MODULE By NICOLÁS ANDRUSKIEWITSCH, ISTVÁN HECKENBERGER, and HANS-JÜRGEN SCHNEIDER

We study the Nichols algebra of a semisimple Yetter-Drinfeld module and introduce new invariants including the notions of real roots and the Weyl groupoid. The crucial ingredient is a “reflection” defined on arbitrary such Nichols algebras. Our construction generalizes the restriction of Lusztig’s automorphisms of quantized Kac-Moody algebras to the nilpotent part. As a direct application we co...

Hans Arnold Heilbronn 1908-1975 Hans