Jörg Feldvoss

Education

• Ph.D. (Dr. rer. nat.) in Mathematics, Hamburg University, July 10, 1989

• High School Teacher Exam for Mathematics and Physics, Hamburg University, May 28, 1986

Research Interests

My research is mainly in Lie Theory and Representation Theory. In particular, I am interested in the following topics:

• Lie and Leibniz (color) algebras: structure, representations, and cohomology

• Lie coalgebras and Lie comodules

• Lie bialgebras and the classical Yang-Baxter equation

• Hochschild (co)homology

• Hopf algebras and tensor categories

• quantum groups at roots of unity

• small quantum groups

• Frobenius algebras

Publications

Books

• (edited with Mahir Bilen Can) A Glimpse into Geometric Representation Theory, Proceedings of the Virtual Special Sessions "Combinatorial and Geometric Representation Theory" and "Cohomology, Representation Theory, and Lie Theory" at the 2021 Fall Southeastern Sectional Meeting of the American Mathematical Society (Meeting #1173), Mobile, AL, November 20 and 21, 2021, Contemp. Math., vol. 804, Amer. Math. Soc., Providence, RI, 2024

• (edited with Lauren Grimley, Drew Lewis, Andrei Pavelescu, and Cornelius Pillen) Advances in Algebra, Proceedings of the Southern Regional Algebra Conference 2017, Mobile, AL, March 17 - 19, 2017, Springer Proceedings in Mathematics and Statistics, vol. 277, Springer, Cham, 2019

• (edited with Marina Avitabile and Thomas Weigel) Lie Algebras and Related Topics, Proceedings of a Workshop on Lie Algebras in Honor of Helmut Strade's 70th Birthday, Università degli Studi di Milano-Bicocca, Milano, Italy, May 22 - 24, 2013, Contemp. Math., vol. 652, Amer. Math. Soc., Providence, RI, 2015

Papers

• (with Friedrich Wagemann) On the cohomology of solvable Leibniz algebras, Indag. Math. 35 (2024), no. 1, 87-113

• (with Friedrich Wagemann) On Leibniz cohomology, J. Algebra 569 (2021), 276-317

• Leibniz algebras as non-associative algebras, in: Nonassociative Mathematics and Its Applications, Denver, CO, 2017 (eds. P. Vojtěchovský, M. R. Bremner, J. S. Carter, A. B. Evans, J. Huerta, M. K. Kinyon, G. E. Moorhouse, J. D. H. Smith), Contemp. Math., vol. 721, Amer. Math. Soc., Providence, RI, 2019, pp. 115-149

• (with Georgia Benkart) Some problems in the representation theory of simple modular Lie algebras, in: Lie Algebras and Related Topics, Milano, Italy, 2013 (eds. M. Avitabile, J. Feldvoss, and Th. Weigel), Contemp. Math., vol. 652, Amer. Math. Soc., Providence, RI, 2015, pp. 207-228

• (with Salvatore Siciliano and Thomas Weigel) Restricted Lie algebras with maximal 0-PIM, Transform. Groups 21 (2016), no. 2, 377-398

• (with Salvatore Siciliano and Thomas Weigel) Split strongly abelian p-chief factors and first degree restricted cohomology, J. Lie Theory 24 (2014), no. 1, 29-39

• (with Salvatore Siciliano and Thomas Weigel) Split abelian chief factors and first degree cohomology for Lie algebras, J. Algebra 382 (2013), 303-313

• (with Sarah Witherspoon) Support varieties and representation type of self-injective algebras, Homology Homotopy Appl. 13 (2011), no. 2, 197-215

• (with Salvatore Siciliano and Thomas Weigel) Outer restricted derivations of nilpotent restricted Lie algebras, Proc. Amer. Math. Soc. 141 (2013), no. 1, 171-179

• (with Sarah Witherspoon) Support varieties and representation type of small quantum groups, Internat. Math. Res. Notices 2010, no. 7, 1346-1362; Erratum, Internat. Math. Res. Notices 2015, no. 1, 288-290

• On the cohomology of modular Lie algebras, in: Lie Algebras, Vertex Operator Algebras and Their Applications, Raleigh, NC, 2005 (eds. Y.-Z. Huang and K. C. Misra), Contemp. Math., vol. 442, Amer. Math. Soc., Providence, RI, 2007, pp. 89-113

• Injective modules and prime ideals of universal enveloping algebras, in: Abelian Groups, Rings, Modules, and Homological Algebra, Auburn, AL, 2004 (eds. P. Goeters and O. M. G. Jenda), Lecture Notes in Pure and Applied Mathematics, vol. 249, Chapman & Hall/CRC, Boca Raton/London/New York, 2006, pp. 107-119

• Existence of triangular Lie bialgebra structures II, J. Pure Appl. Algebra 198 (2005), no. 1-3, 151-163

• On polynomials of sums of powers (in German), Mitt. Math. Ges. Hamburg 20 (2001), 115-124

• Existence of solutions of the classical Yang-Baxter equation for a real Lie algebra, Abh. Math. Sem. Univ. Hamburg 71 (2001), 297-304

• On the number of simple modules of a supersolvable restricted Lie algebra, J. Algebra 230 (2000), no. 2, 319-333

• Projective modules and blocks of supersolvable restricted Lie algebras, J. Algebra 222 (1999), no. 1, 284-300

• Representations of Lie colour algebras, Adv. Math. 157 (2001), no. 2, 95-137

• (with Daniel Nakano) Representation theory of the Witt algebra, J. Algebra 203 (1998), no. 2, 447-469

• Chief factors and the principal block of a restricted Lie algebra, in: The Monster and Lie Algebras, Columbus, OH, 1996 (eds. J. C. Ferrar and K. Harada), Ohio State Univ. Math. Res. Inst. Publ., vol. 7, Walter de Gruyter, Berlin, 1998, pp. 187-194

• (with Lee Klingler) Tensor powers and projective modules for Hopf algebras, in: Algebras and Modules II, Geiranger, Norway, 1996 (eds. I. Reiten, S. O. Smalø, and Ø. Solberg), Canad. Math. Soc. Conf. Proc., vol. 24, Amer. Math. Soc., Providence, RI, 1998, pp. 195-203

• Existence of triangular Lie bialgebra structures, J. Pure Appl. Algebra 134 (1999), no. 1, 1-14

• Homological topics in the representation theory of restricted Lie algebras, in: Lie Algebras and Their Representations, Seoul, South Korea, 1995 (eds. S.-J. Kang, M.-H. Kim, and I. Lee), Contemp. Math., vol. 194, Amer. Math. Soc., Providence, RI, 1996, pp. 69-119

• On the block structure of supersolvable restricted Lie algebras, J. Algebra 183 (1996), no. 2, 396-419

• Blocks and projective modules for reduced universal enveloping algebras of a nilpotent restricted Lie algebra, Arch. Math. (Basel) 65 (1995), no. 6, 495-500

• A cohomological characterization of solvable modular Lie algebras, in: Non-Associative Algebra and Its Applications, Oviedo, Spain, 1993 (ed. S. González), Mathematics and Its Applications, vol. 303, Kluwer Academic Publishers, Dordrecht/Boston/London, 1994, pp. 133-139

• (with Detlef Günzel) On the curvature of symmetric coupler curves (in German), Konstruktion 44 (1992), no. 3, 99-104

• (with Helmut Strade) Restricted Lie algebras with bounded cohomology and related classes of algebras, Manuscripta Math. 74 (1992), no. 1, 47-67

• On the cohomology of restricted Lie algebras, Comm. Algebra 19 (1991), no. 10, 2865-2906

• (with Wolfram Funk and Peter Tolle) A contribution to the classification of coupler curves (in German), in: Proceedings of the 8th World Congress on the Theory of Machines and Mechanisms, Prague, Czech Republic, 1991, vol. 4, pp. 1161-1164