Jun. Prof. Simon Lentner

Algebra and Number Theory (AZ), University Hamburg

Bundesstraße 55, 20146 Hamburg

+49 (0)40 42838 5194

simon.lentner@uni-hamburg.de

PDF: CV, Publications, Talks, Teaching

**PUBLICATIONS AND PREPRINTS: (all publication on arXiv)**

** Hochschild Cohomology, Modular Tensor Categories, and Mapping Class Groups (with S. Mierach, C. Schweigert, Y. Sommerhäuser).**

accepted for Springer Briefs in Mathematical Physics, arXiv:2003.06527

Algebras of non-local screenings and diagonal Nichols algebras (with I. Flandoli).

Preprint (2019), arXiv:1911.11040

On Borel subalgebras of quantum groups (with K. Vocke).

Preprint (2019), arXiv:1905.05867

** Modularization of small quantum groups (with A. Gainudtinov, T. Ohrmann),**Preprint (2018),

**arXiv:1809.02116**

Hochschild Cohomology and the Modular Group (with S. Mierach, C. Schweigert, Y. Sommerhäuser).

Journal of Algebra 507 (2018) pp. 400-420, arXiv:1707.04032

Logarithmic conformal field theories of type Bn, l=4 and symplectic fermions (with I. Flandoli)

Journal of Mathematical Physics 59 (2018), arXiv:1706.07994

**Quantum groups and Nichols algebras acting on conformal field theories,**

accepted for Advances in Mathematics, arXiv: 1702.06431

The unrolled quantum group inside Lusztig's quantum group of divided powers,

Letters in Mathematical Physics 109/7 (2019), p. 1665-1682, arXiv:1702.05164

**Three natural subgroups of the Brauer-Picard group of a Hopf algebra with applications** (with J. Priel),

Bull. Belg. Math. Soc. Simon Stevin 24 (2017), p. 73-106. arXiv:1702.05133

Factorizable R-matrices for small quantum groups (with T. Ohrmann),

SIGMA 13 (2017). arXiv:1612.07960

A decomposition of the Brauer-Picard group of the representation category of a finite group (with J. Priel),

Journal of Algebra 489 (2017), p. 264-309, arXiv:1506.07832

On monoidal autoequivalences of the category of Yetter-Drinfeld modules over a group: The lazy case (with J. Priel)

Algebra and Representation Theory 22/4 (2018), p. 1017-1049, arXiv:1511.03871

Nash Equilibria And Partition Functions Of Games With Many Dependent Players (with E. Kraus, Munich),

Preprint (2015), arXiv:1504.03965

**A simplicial complex of Nichols algebras** (with M. Cuntz, Hannover),

Mathematische Zeitschrift 285, 3-4 (2017) p. 647-683. arXiv:1503.08117

Quantum affine algebras at small root of unity,

Preprint (2014), arXiv:1411.2959

New R-matrices for small quantum groups (with D. Nett, Hamburg),

Algebras and Representation Theory 18/6 (2015), p. 1649-1673. arXiv:1409.5824

A theorem on roots of unity and a combinatorial principle (with D. Nett, Hamburg), Preprint (2014), arXiv:1409.5822

**A Frobenius homomorphism for Lusztig's quantum groups over arbitrary roots of unity**,

Communications in Contemporary Mathematics 18/3 (2015). arXiv:1406.0865.

Factorization Of Graded Traces On Nichols Algebras (with Dr. Lochmann, Marburg),

Axioms, 6/4, Special Issue Hopf Algebras, Quantum Groups and Yang–Baxter Equations 2017, arXiv:1403.4287.

Partially Dualized Hopf Algebras Have Equivalent Yetter-Drinfel'd Modules (with A. Barvels und C. Schweigert, Hamburg),

Journal of Algebra 430 (2015) p. 303-342, arXiv:1402.221.

Root Systems In Finite Symplectic Vector Space,

Communications in Algebra, 43 (2015) p. 4446-4470. arXiv:1307.7151.

**New Large-Rank Nichols Algebras Over Nonab. Groups With Commutator Subgroup Z_2**,

Journal of Algebra 419 (2014) p. 1-33. arXiv:1306.5684.

**THESES:**

Orbifoldizing Hopf- and Nichols Algebras,

PhD-Thesis, LMU Munich, 2012.

Vertex Algebras Constructed from Hopf Algebra Structures,

Diploma-Thesis, LMU Munich, 2007.