About Me
I am a mathematician. I am interested in algebra. In particular groups, finite-dimensional algebras and their representation theory.
Interests
- Group representations
- Finite and profinite groups
- Finite-dimensional algebras
- Lattices and orders
- Hochschild cohomology
- Deformation theory
- $\tau$-tilting and silting theory
- Picard groups
- Unit groups
- Computer algebra
Education
-
PhD in Mathematics, 2012
RWTH Aachen University
-
Diplom in Mathematics, 2008
RWTH Aachen University
Publications
(2024).
Units in Blocks of Defect 1 and the Zassenhaus Conjecture.
Rev. Mat. Complut., to appear.
(2022).
Arbitrarily large Morita Frobenius numbers.
Algebra & Number Theory, Vol. 16, No. 8, 1889–1904.
(2022).
Bijections of silting complexes and derived Picard groups.
J. London Math. Soc., 106: 1008-1060.
(2021).
On the geometry of lattices and finiteness of Picard groups.
J. Reine Angew. Math. (Crelle’s journal) 782, 219–233.
(2020).
The Picard group of an order and Külshammer reduction.
Algebr. Represent. Th. 24, pages 505–518.
(2019).
On solvability of the first Hochschild cohomology of a finite-dimensional algebra.
Trans. Amer. Math. Soc. 373, 7607-7638.
(2019).
Donovan's conjecture, blocks with abelian defect groups and discrete valuation rings.
Math Z., Vol. 295, Pages 249–264.
(2018).
A Counterexample to the First Zassenhaus Conjecture.
Adv. Math., Vol. 339, Pages 599-641.
(2018).
A reduction theorem for $\tau$-rigid modules.
Math Z., Vol. 290, Issue 3–4, Pages 1377–1413.
(2017).
On Tate duality and a projective scalar property for symmetric algebras.
Pacific J. Math. Vol. 293 (2018), No. 2, 277–300.
(2016).
Blocks with a generalized quaternion defect group and three simple modules over a 2-adic ring.
J. Algebra, Volume 456, Pages 294-322.
(2015).
Describing units of integral group rings up to commensurability.
J. Pure Appl. Algebra, Volume 219, Issue 7, Pages 2901-2916.
(2014).
The $p$-adic group ring of ${\rm SL}_2(p^f)$.
J. Algebra, Volume 410, Pages 421-459.
(2014).
Basic Orders for Defect Two Blocks of $\mathbb Z_p\Sigma_n$.
Comm. Algebra, Volume 42, Issue 7, Pages 2890-2907.
(2013).
On the IYB-property in some solvable groups.
Arch. Math., Volume 101, Issue 4, Pages 309–318.
(2012).
$p$-Adic lifting problems and derived equivalences.
J. Algebra, Volume 356, Issue 1, Pages 90-114.
Preprints & Unpublished Notes
(2024).
Units in group rings and blocks of Klein four or dihedral defect.
preprint.
(2023).
A counterexample to a conjecture on Cartan determinants of monoid algebras.
note (not intended for publication).
Theses
- PhD thesis: Group rings over the $p$-adic integers, March 2012.
- Diplom thesis: Algorithmische Behandlung $p$-adischer ganzzahliger Gruppenringe (in German), October 2008.
GAP Code
The “orders” package
This package allows to compute with orders over the $p$-adic integers, such as $\mathbb Z_p G$ for a finite group $G$. Among other things it can compute indecomposable projective lattices and basic algebras. Most of it was written back in 2009 while I was working on my master’s thesis, but I added functionality over the last few years, as needed for my research.
- Repository: https://github.com/feisele/orders/
- Download: orders-1.02.tar.gz (just unpack this in the
pkg/directory of your GAP installation and useLoadPackage("orders");)
Miscellaneous
- I co-organised the conference Algebra and Number Theory In Conversation (ANTIC) in Manchester, September 2023.
- I co-organised the conference Structure of Group Algebras over Local Rings in Ambleside, August 2022.
Contact
| florian.eisele@manchester.ac.uk | |
|---|---|
| +44 161 275 5838 | |
| Room 2.120, Alan Turing Building, Department of Mathematics, University of Manchester, Oxford Road, Manchester, M13 9PL |