Rolf Farnsteiner

Algebraic Lie Theory and Representation Theory

The Research Team

Professor

Rolf Farnsteiner (Representations of algebraic groups, support spaces, Auslander-Reiten theory, homological algebra)

Postdoctoral Researcher
Daniel Bissinger (Representations of quivers, Gabriel-Roiter measures)

 

PhD-Student
Jie Liu (Representations of algebraic groups)

Master's Students

Malte Frömming (Geometric invariants for representations of restricted Lie algebras)
Bendikt Karrasch (Representation type of group algebras)
Jan-Niclas Thiel (Algebraic groups and modular Lie algebras)

 

Former Members

Postdocs and Ph.D.-Students:

Gil Vernik (now research staff member at IBM Haifa Research Lab)
Julian Külshammer (now post-doc (Assistent) at the University of Stuttgart)
Jean-Marie Bois  (Lie theory, representation theory, non-commutative algebras and division rings)
Julia Worch (now at Rüss, Dr. Zimmermann und Partner)
Daiva Pucinskaite (now Visiting Assistant Professor at Florida Atlantic University)
       Dirk Kirchhoff (now at Heidelberger Druckmaschinen)

Hao Chang (now Associate Professor at Central China Normal University) 
Christian Drenkhahn (now at Rüss, Dr. Zimmermann und Partner)
Yang Pan (now Lecturer at Zhejiang Agriculture and Forestry University)

Master's Students:

Christine Munstermann (now teacher at Hans-Brüggemann-Schule
Andreas Gundrum (now at Acando GmbH)

Publications

In the lists below, article links to the published version and pdf to a preprint version.

  • J. Külshammer, Biserial algebras via subalgebras and the path algebra of D4, J. Algebra 331 (2011), 58 – 67. article
  • R. Farnsteiner, Lie algebras with a coalgebra splitting, Algebr. Represent. Theory 14 (2011), 87 – 96. article, pdf
  • R. Farnsteiner and G. Röhrle, Support varieties, AR-components and good filtrations, Math. Z. 267 (2011), 185 – 219. article, pdf
  • J.-M. Bois and G. Vernik, Algebraic families of subfields in division rings, J. Algebra 339 (2011), 172 – 180. article, pdf
  • R. Farnsteiner, Combinatorial and geometric aspects of the representation theory of finite algebraic groups, In: Lie Theory and Representation Theory.
    Surveys of  Modern Mathematics 2 (2012), 47-144. pdf
  • R. Farnsteiner, Complexity, periodicity and one-parameter subgroups, Trans. Amer. Math. Soc. 365 (2013), 1487-1531. pdf
  • D. Pučinskaitė, 1-quasi-hereditary algebras, J. London Math. Soc. 87 (2013), 478-496. pdf
  • J. Külshammer, Representation type of Frobenius-Lusztig kernels, Quart. J. Math. 64 (2013), 471-488. pdf
  • J. Worch, Categories of modules for elementary abelian p-groups and generalized Beilinson algebras,  J. London Math. Soc. 88 (2013), 649-668. pdf
  • J. Külshammer, Auslander-Reiten theory of Frobenius-Lusztig kernels. Bull. London Math. Soc. 45 (2013), 1285-1300. pdf
  • J. Külshammer, Auslander-Reiten theory of small quantum groups. Proc. Amer. Math. Soc. 142 (2014), 1109-1119. pdf
  • R. Farnsteiner, Jordan types for indecomposable modules of finite group schemes. J. Eur. Math. Soc. 16 (2014), 925-989. pdf
  • J.M. Bois, R. Farnsteiner, B. Shu, Weyl groups for non-classical restricted Lie algebras, and the Chevalley restriction theorem. Forum Math. 26 (2014), 1333-1380. pdf
  • R. Farnsteiner, Extensions of tame algebras and finite group schemes of domestic representation type. Forum Math. 27 (2015), 1071-1100. pdf 
  • D. Pučinskaitė, Quasi-hereditary algebras via generator-cogenerators of local self-injective algebras and transfer of Ringel duality. Math. Z. 279 (2015), 641-668. pdf
  • J. Worch, AR-Components for generalized Beilinson algebras. Proc. Amer. Math. Soc. 143 (2015), 4271-4281. pdf
  • H. Chang, Adjoint quotient maps for the restricted Lie algebras Wn and Sn. Commun. Algebra 45 (2017), 47-59.  pdf
  • R. Farnsteiner, Representations of finite group schemes and morphisms of projective varieties. Proc. London Math. Soc. 114 (2017), 433-475.  pdf
  • Ch. Drenkhahn, On simple polynomial GrT-modules. J. Algebra 486 (2017), 1-13.  pdf
  • D. Kirchhoff, Classification of indecomposable modules for finite group schemes of domestic representation type. Transform. Groups 22 (2017), 1005-1029.  pdf
  • Y. Pan, Varieties of elementary subalgebras of submaximal rank in type A. J. Lie Theory 28 (2018), 57-70.  pdf
  • Ch. Drenkhahn, Almost split sequences for polynomial GrT-modules and polynomial parts of Auslander-Reiten components. J. Pure Appl. Algebra 222 (2018), 155-180 pdf
  • D. Bissinger, Representations of regular trees and invariants of AR-components for generalized Kronecker quivers. Algebr. Represent. Theory (to appear)  pdf
  • Y. Pan, Saturation rank for finite group schemes: Finite groups and infinitesimal group schemes. Forum Math. (to appear) pdf
  • D. Kirchhoff,  AR-components of  domestic finite group schemes: McKay-quivers and ramification. Quart. J. Math. (to appear) pdf
  • H. Chang and R. Farnsteiner, Finite group schemes of p-rank ≤ 1. Math. Proc. Cambridge Phil. Soc. (to appear)   pdf

 

Preprints

  • R. Farnsteiner, Categories of modules given by varieties of nilpotent operators. pdf
  • D. Pučinskaitė, 1-quasi-hereditary algebras. Examples and invariant submodules of projectives. pdf
  • D. Bissinger, Representations of constant socle rank for the Kronecker algebra. pdf
  • H. Chang and R. Farnsteiner, Varieties of elementary abelian Lie algebras and degrees of modulespdf