1 citations · 3 across the 7 of their papers we have counts for
9 papers
Gabi-Monads
Sebastian Halbig, Paolo Saracco, Tony Zorman
We study gabi-monads on skew-closed categories, extending the gabi-algebras of Berger, the second author, and Vercruysse beyond the linear case. Our main reconstruction theorem ide…
Irreducible representations of generalised Kac-Paljutkin Hopf algebras
Sebastian Halbig, Christian Lomp
The aim of this note is to provide a self-contained classification of the irreducible representations of generalised Kac--Paljutkin Hopf algebras, recently introduced by the second…
A non-semisimple Kitaev lattice model
Sebastian Halbig, Ulrich Krähmer
The construction of the topologically protected code space of Kitaev's model for fault-tolerant quantum computation is extended from complex semisimple to arbitrary finite-dimensio…
Diagrammatics for Comodule Monads
Sebastian Halbig, Tony Zorman
We extend Willerton's graphical calculus for bimonads to comodule monads, a monadic interpretation of module categories over a monoidal category. As an application, we prove a vers…
Categorical centers and Yetter--Drinfel`d-modules as 2-categorical (bi)lax structures
Bojana Femić, Sebastian Halbig
The bicategorical point of view provides a natural setting for many concepts in the representation theory of monoidal categories. We show that centers of twisted bimodule categorie…
Duality in Monoidal Categories
Sebastian Halbig, Tony Zorman
We compare closed and rigid monoidal categories. Closedness is defined by the tensor product having a right adjoint: the internal hom functor. Rigidity, on the other hand, generali…
Pivotality, twisted centres and the anti-double of a Hopf monad
Sebastian Halbig, Tony Zorman
Finite-dimensional Hopf algebras admit a correspondence between so-called pairs in involution, one-dimensional anti-Yetter--Drinfeld modules and algebra isomorphisms between the Dr…
Generalised Taft algebras and pairs in involution
Sebastian Halbig
A class of finite-dimensional Hopf algebras which generalise the notion of Taft algebras is studied. We give necessary and sufficient conditions for these Hopf algebras to omit a p…
A Hopf algebra without modular pair in involution
Sebastian Halbig, Ulrich Kraehmer
The aim of this short note is to communicate an example of a finite-dimensional Hopf algebra that does not admit a modular pair in involution in the sense of Connes and Moscovici.