20 citations · 39 across the 6 of their papers we have counts for
9 papers · 1 filter
Right coideal subalgebras of the Borel part of a quantized enveloping algebra
I. Heckenberger, S. Kolb
For the Borel part of a quantized enveloping algebra we classify all right coideal subalgebras for which the intersection with the coradical is a Hopf algebra. The result is expres…
Drinfel'd doubles and Shapovalov determinants
I. Heckenberger, H. Yamane
The Shapovalov determinant for a class of pointed Hopf algebras is calculated, including quantized enveloping algebras, Lusztig's small quantum groups, and quantized Lie superalgeb…
Root systems and Weyl groupoids for Nichols algebras
I. Heckenberger, H. -J. Schneider
Motivated by work of Kac and Lusztig, we define a root system and a Weyl groupoid for a large class of semisimple Yetter-Drinfeld modules over an arbitrary Hopf algebra. The obtain…
Lusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type
I. Heckenberger
In the structure theory of quantized enveloping algebras, the algebra isomorphisms determined by Lusztig led to the first general construction of PBW bases of these algebras. Also,…
De Rham Complex for Quantized Irreducible Flag Manifolds
I. Heckenberger, S. Kolb
It is shown that quantized irreducible flag manifolds possess a canonical -analogue of the de Rham complex. Generalizing the well known situation for the standard Podleś' quantu…
Podleś' Quantum Sphere: Dual Coalgebra and Classification of Covariant First Order Differential Calculus
I. Heckenberger, S. Kolb
The dual coalgebra of Podleś' quantum sphere O_q(S^2_c) is determined explicitly. This result is used to classify all finite dimensional covariant first order differential calculi…