Rolf Farnsteiner

Research

Visitors

Seminar Bremen-Hamburg-Kiel
The Research-Team

Fields of Interest

Algebraic Lie Theory and Representation Theory

Algebraic Groups
Modular Lie Algebras
Universal Enveloping Algebras
Representations of Associative Algebras (Auslander-Reiten Theory)
Module Varieties (Support Varieties, Rank Varieties, p-Points)  

Homological Algebra

Homology of Associative Algebras
Ordinary and Restricted Cohomology of Restricted Lie Algebras

Project

Combinatorial and Geometric Aspects of the Representation Theory of Finite Group Schemes (2009-2015) (pdf-file)dfglogo.gif

 

 

Publications and Lectures

Preprints and Recent Papers

  • Group-graded algebras, extensions of infinitesimal groups, and applications. (ps-file, pdf-file)
    Transform. Groups 14 (2009), 127-162
  • Lie algebras with a coalgebra splitting. (ps-file, pdf-file)
    Algebr. Represent. Theory 14 (2011), 87-96
  • Support varieties, AR-components and good filtrations. (with Gerhard Röhrle) (pdf-file)
    Math. Z. 267 (2011), 185-219
  • Combinatorial and geometric aspects of the representation theory of finite algebraic groups (pdf-file)
    In: Lie Theory and Representation Theory. Surveys of  Modern Mathematics 2 (2012), 47-144
  • Complexity, periodicity and one-parameter subgroups (pdf-file)
    Trans. Amer. Math. Soc. 365 (2013), 1487-1531
  • Dynkin diagrams, support spaces and representation type. (pdf-file)
    Note Mat. 33 (2013), 49-69
  • Jordan types for indecomposable modules of finite group schemes (pdf-file)
    J. Eur. Math. Soc. 16 (2014), 925-989
  • Weyl groups for non-classical restricted Lie algebras and the Chevalley restriction theorem. (with Jean-Marie Bois and Bin Shu) (pdf-file)  Forum Math. 26 (2014), 1333-1379
  • Extensions of tame algebras and finite group schemes of domestic representation type. (pdf-file)
    Forum Math. 27 (2015), 1071-1100
  • Representations of finite group schemes and morphisms of projective varieties. (pdf-file)
    Proc. London Math. Soc. 114 (2017), 433-475
  • Finite group schemes of p-rank ≤ 1. (with H. Chang) (  pdf-file)
    Math. Proc. Cambridge Phil. Soc. (to appear)
  • Varieties of elementary abelian Lie algebras and degrees of modules. (with H. Chang) (pdf-file)
  • Categories of modules given by varieties of p-nilpotent operators. (pdf-file)

 

Publications 1999 - 2008

  1. Representations of nilpotent Lie algebras.
    Arch. Math. 72 (1999), 28-39
  2. On support varieties of Auslander-Reiten components.
    Indag. Math. 10 (1999), 221-234
  3. On Auslander-Reiten quivers of enveloping algebras of restricted Lie algebras.
    Math. Nachr. 202 (1999), 43-66
  4. Modules of solvable infinitesimal groups and the structure of representation-finite
    cocommutative Hopf algebras. Math. Proc. Cambridge Phil. Soc. 127 (1999), 441-459  (with Detlef Voigt)
  5. On cocommutative Hopf algebras of finite representation type.
    Adv. in Math. 155 (2000), 1-22  (with Detlef Voigt)
  6. Auslander-Reiten components for Lie algebras of reductive groups.
    Adv. in Math. 155 (2000), 49-83
  7. On the Auslander-Reiten quiver of an infinitesimal group.
    Nagoya Math. J. 160 (2000), 103-121
  8. Schemes of tori and the structure of tame restricted Lie algebras.
    J. London Math. Soc. 63 (2001), 553-570  (with Detlef Voigt)
  9. Infinitesimal unipotent group schemes of complexity 1.
    Colloq. Math. 89 (2001), 179-192  (with Gerhard Röhrle and Detlef Voigt)
  10. Representations of infinitesimal groups of characteristic 2.
    Arch. Math. 78 (2002), 184-188  (with Detlef Voigt)
  11. Almost split sequences of Verma modules.
    Math. Ann. 322 (2002), 701-743  (with Gerhard Röhrle )
  12. Classification of restricted Lie algebras with tame principal block.
    J. reine angew. Math. 546 (2002), 1-45  (with Andrzej Skowronski)
  13. On infinitesimal groups of tame representation type.
    Math. Z. 244 (2003), 479-513  (with Detlef Voigt)
  14. Varieties of tori and Cartan subalgebras of restricted Lie algebras.
    Trans. Amer. Math. Soc. 356 (2004), 4181-4236
  15. Block representation type of Frobenius kernels of smooth groups. (ps-file, pdf-file)
    J. reine angew. Math. 586 (2005), 45-69
  16. Auslander-Reiten components for G1T-modules. (ps-file, pdf-file)
    J. Algebra Appl. 4 (2005), 739-759
  17. The tame infinitesimal groups of odd characteristic. (ps-file, pdf-file)
    Adv. in Math. 205 (2006), 229-274   (with Andrzej Skowronski)
  18. Polyhedral Groups, McKay Quivers, and the Finite Algebraic Groups with Tame Principal Blocks. (ps-file, pdf-file)
    Invent. math. 166 (2006), 27-94
  19. Tameness and Complexity of Finite Group Schemes. (ps-file, pdf-file)
    Bull. London Math. Soc. 39 (2007), 63-70
  20. Galois Actions and Blocks of Tame Infinitesimal Group Schemes. (with Andrzej Skowronski) (ps-file, pdf-file)
    Trans. Amer. Math. Soc. 359 (2007), 5867-5898
  21. Support Spaces and Auslander-Reiten Components. (ps-file, pdf-file)
    Contemp. Math. 442 (2007), 61-87

 

Publications 1989 - 1998

  1. Lie Theoretic Methods in Cohomology Theory.
    Lecture Notes in Mathematics 1373 (1989), 93-110
  2. Extension Functors of Modular Lie Algebras.
    Math. Ann. 288 (1990), 713-730
  3. Cohomology Groups of Reduced Enveloping Algebras.
    Math. Z. 206 (1991), 103-117
  4. Shapiro's Lemma and its Consequences in the Cohomology Theory of Modular Lie Algebras.
    Math. Z. 206 (1991), 153-168   (with H. Strade)
  5. On the Cohomology of Ring Extensions.
    Adv. in Math. 87 (1991), 42-70
  6. Recent Developments in the Cohomology Theory of Modular Lie Algebras.
    In:  Nonassociative Algebras and Related Topics,  K. Yamaguti, N. Kawamoto (Eds.)  World Scientific 1991,  19-46
  7. On the Theory of Frobenius Extensions and its Application to Lie Superalgebras.
    Trans. Amer. Math. Soc. 335 (1993), 407-424 (with Allen Bell)
  8. On Frobenius Extensions Defined by Hopf Algebras.
    J. Algebra 166 (1994), 130-141
  9. Representations of Reduced Enveloping Algebras.
    In: Non-Associative Algebra and its Applications, S. Gonzales, (ed.), Mathematics and Its Applications 303 (1994), 128-133
  10. Representations of Lie Algebras with Triangular Decomposition.
    Symposia Gaussiana 2 (1995), 275-286
  11. Periodicity and Representation Type of Modular Lie Algebras.
    J. reine angew. Math. 464 (1995), 47-65
  12. Representations of Blocks Associated to Induced Modules of Restricted Lie Algebras.
    Math. Nachr. 179 (1996), 57-88
  13. Note on Frobenius Extensions and Restricted Lie Superalgebras.
    J. Pure Appl. Algebra 108 (1996), 241-256
  14. Auslander-Reiten Theory for Restricted Lie Algebras.
    Ohio State Mathematical Research Institute Publications 7 (1998), 165-186
  15. On the Distribution of AR-Components of Restricted Lie Algebras.
    Contemp. Math. 229 (1998), 139-157

 

Publications 1981 - 1988

  1. Lie Algebras with Faithful Completely Reducible Representations.
    Abh. Math. Sem. Univ. Hamburg 51 (1981), 244-251  (with H. Strade)
  2. On Ad-Semisimple Lie Algebras.
    J. Algebra 83 (1983), 510-519
  3. On the Structure of Simple-Semiabelian Lie Algebras
    Pac. J. Math. 111 (1984), 287-299
  4. Quaternionic Lie Algebras.
    Lin. Alg. Appl. 61 (1984), 225-231
  5. Restricted Lie Algebras with Semilinear p-Mappings.
    Proc. Amer. Math. Soc. 91 (1984), 41-45
  6. Conditions for the Commutativity of Restricted Lie Algebras.
    Comm. Algebra 13 (1985), 1475-1489
  7. Ad-Semisimple Lie Algebras and their Applications.
    Canad. Math. Soc. Conf. Proc 5 (1986), 219-225
  8. The Associative Forms of the Graded Cartan Type Lie Algebras.
    Trans. Amer. Math. Soc. 295 (1986), 417-427
  9. Central Extensions and Invariant Forms of Graded Lie Algebras.
    Algebras, Groups, Geom. 3 (1986), 431-455
  10. Dual Space Derivations and H2(L,F) of Modular Lie Algebras.
    Canad. J. Math. 39 (1987), 1087-1106
  11. On the Cohomology of Associative Algebras and Lie Algebras.
    Proc. Amer. Math. Soc. 99 (1987), 415-420
  12. On the Vanishing of Homology and Cohomology Groups of Associative Algebras.
    Trans. Amer. Math. Soc. 306 (1988), 651-665
  13. Derivations and Central Extensions of Finitely Generated Graded Lie Algebras.
    J. Algebra  118 (1988), 33-45
  14. On the Derived Length of Solvable Lie Algebras.
    Math. Ann. 282 (1988),  503-511  (with H. Strade)
  15. Cohomology Groups of Infinite Dimensional Algebras.
    Math. Z. 199 (1988), 407-423
  16. Modular Lie Algebras and their Representations.
    Marcel Dekker Monographs Vol. 116  New York 1988  (with H. Strade)

 

Lectures

  • Conference on Frobenius Algebras and Related Topics, Torun, September 2003
    Lecture Series: ''Subgroup Varieties and Representations of Infinitesimal Groups" (pdf-file)
  • University of Bielefeld, April 2007
    Lecture Series: "Support Varieties, p-Points and Jordan Type" (pdf-file)
  • Isaac Newton Institute Cambridge, March 2009
    Lecture: "Support Spaces, Jordan Types and Indecomposable Modules" (pdf-file)
  • University of Bielefeld, April 2009
    Lecture Series: "Support Varieties, AR-Components and Good Filtrations" (pdf-file)
  • Conference on Advances in Group Theory and Application, Lecce, June 2011
    Lecture Series: "Dynkin Diagrams, Support Spaces and Representation Type" (Lecture I, Lecture II, Lecture III)
  • Third Summer School and Workshop on Lie Theory and Representation Theory, ECNU, Shanghai, June 2012
    Lecture Series: ''Nilpotent Operators, Categories of Modules, and Auslander-Reiten Theory'' (pdf-file)

 

 

Editorships

The Open Mathematics Journal

ISRN Geometry