25 citations · 94 across the 25 of their papers we have counts for
35 papers
Higher Fomin-Kirillov algebras are infinite-dimensional
N. Andruskiewitsch, I. Angiono, I. Heckenberger +3
We show that the Fomin--Kirillov algebras are infinite-dimensional for . This answers a question posed by Fomin and Kirillov in 1997. To prove this, we demonstrate t…
Affine at admissible levels and quantum
Thomas Creutzig, Simon D. Lentner
We prove braided tensor equivalences between the categories of weight modules of the affine vertex algebra of at any admissible level and categories associated to…
Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups II
Simon Lentner, Svea Nora Mierach, Christoph Schweigert +1
In the first part of this work, we have, for a not necessarily semisimple modular category, generalized the action of the mapping class groups of surfaces on the spaces of conforma…
A conditional algebraic proof of the logarithmic Kazhdan-Lusztig correspondence
Simon D. Lentner
The logarithmic Kazhdan-Lusztig correspondence is a conjectural equivalence between braided tensor categories of representations of small quantum groups and representations of cert…
Modular -Crossed Tambara-Yamagami-like Categories for Even Groups
César Galindo, Simon Lentner, Sven Möller
We explicitly construct nondegenerate braided -crossed tensor categories of the form . They are -…
Computing -Crossed Extensions and Orbifolds of Vertex Operator Algebras
César Galindo, Simon Lentner, Sven Möller
In this article, we develop tools for computing -crossed extensions of braided tensor categories. Their equivariantisations appear as categories of modules of fixed-point subalg…
Fibre functors and reconstruction of Hopf algebras
Simon Lentner, Martín Mombelli
The main objective of the present paper is to present a version of the Tannaka-Krein type reconstruction Theorems: If is an exact faithful monoidal functor of tensor cat…
An algebraic theory for logarithmic Kazhdan-Lusztig correspondences
Thomas Creutzig, Simon Lentner, Matthew Rupert
Let be a braided tensor category, typically unknown, complicated and in particular non-semisimple. We characterize under the assumption that there exist…
Vertex algebras with big center and a Kazhdan-Lusztig Correspondence
Boris L. Feigin, Simon D. Lentner
Certain deformable families of vertex algebras acquire at a limit of the deformation parameter a large center, similar to affine Lie algebras at critical level. Then the vertex alg…
Pointed Hopf algebras over non-abelian groups with non-simple standard braidings
Iván Angiono, Simon Lentner, Guillermo Sanmarco
We construct finite-dimensional Hopf algebras whose coradical is the group algebra of a central extension of an abelian group. They fall into families associated to a semisimple Li…
Duality structures for module categories of vertex operator algebras and the Feigin Fuchs boson
Robert Allen, Simon Lentner, Christoph Schweigert +1
Huang, Lepowsky and Zhang have developed a module theory for vertex operator algebras that endows suitably chosen module categories with the structure of braided monoidal categorie…
Characterizing braided tensor categories associated to logarithmic vertex operator algebras
Thomas Creutzig, Simon Lentner, Matthew Rupert
Given a non-semisimple braided tensor category, with oplax tensor functors from known braided tensor categories, we ask : How does this knowledge characterize the tensor product an…
Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups
Simon Lentner, Svea Nora Mierach, Christoph Schweigert +1
Given a finite modular tensor category, we associate with each compact surface with boundary a cochain complex in such a way that the mapping class group of the surface acts projec…
Algebras of Non-Local Screenings and Diagonal Nichols Algebras
Ilaria Flandoli, Simon D. Lentner
In a vertex algebra setting, we consider non-local screening operators associated to the basis of any non-integral lattice. We have previously shown that, under certain restriction…
On Borel subalgebras of quantum groups
Simon D. Lentner, Karolina Vocke
For a quantum group, we study those right coideal subalgebras, for which all irreducible representations are one-dimensional. If a right coideal subalgebra is maximal with this pro…
Modularization of small quantum groups
Azat M. Gainutdinov, Simon Lentner, Tobias Ohrmann
We construct a large family of ribbon quasi-Hopf algebras related to small quantum groups, with a factorizable R-matrix. Our main purpose is to obtain non-semisimple modular tensor…
Hochschild Cohomology and the Modular Group
Simon Lentner, Svea Nora Mierach, Christoph Schweigert +1
It has been shown in previous work that the modular group acts projectively on the center of a factorizable ribbon Hopf algebra. The center is the zeroth Hochschild cohomology grou…
Logarithmic conformal field theories of type and symplectic fermions
I. Flandoli, S. Lentner
There are important conjectures about logarithmic conformal field theories (LCFT), which are constructed as kernel of screening operators acting on the vertex algebra of the rescal…
Three natural subgroups of the Brauer-Picard group of a Hopf algebra with applications
Simon D. Lentner, Jan Priel
In this article we construct three explicit natural subgroups of the Brauer-Picard group of the category of representations of a finite-dimensional Hopf algebra. In examples the Br…
Quantum groups and Nichols algebras acting on conformal field theories
Simon D. Lentner
We prove that certain screening operators in conformal field theory obey the algebra relations of a corresponding Nichols algebra with diagonal braiding. Our result proves in parti…
A family of new Borel subalgebras of quantum groups
S. Lentner, K. Vocke
We construct a family of right coideal subalgebras of quantum groups, which have the property that all irreducible representations are one-dimensional, and which are maximal with t…
The unrolled quantum group inside Lusztig's quantum group of divided powers
Simon D. Lentner
In this letter we prove that the unrolled small quantum group, appearing in quantum topology, is a Hopf subalgebra of Lusztig's quantum group of divided powers. We do so by writing…
Factorizable -Matrices for Small Quantum Groups
Simon Lentner, Tobias Ohrmann
Representations of small quantum groups at a root of unity and their extensions provide interesting tensor categories, that appear in different areas of algeb…
On monoidal autoequivalences of the category of Yetter-Drinfeld modules over a group: The lazy case
Simon Lentner, Jan Priel
An interesting open question is to determine the group of monoidal autoequivalences of the category of Yetter-Drinfeld modules over a finite group , or equivalently the group of…