Publications

• (with H. Yamane) Drinfel'd doubles and Shapovalov determinants
  Preprint, October 2008
• (with H.-J. Schneider) Root systems and Weyl groupoids for Nichols algebras
  Preprint, July 2008
• (with M. Cuntz) Weyl groupoids of rank two and continued fractions
  Preprint, July 2008
• (with M. Cuntz) Weyl groupoids with at most three objects
  Preprint, May 2008. Accepted for publication in J. Pure Appl. Algebra
• (with N. Andruskiewitsch and H.-J. Schneider) The Nichols algebra of a semisimple Yetter-Drinfeld module
  Preprint, March 2008
• Lusztig isomorphisms for Drinfel'd doubles of Nichols algebras of diagonal type
  Preprint, October 2007
• (with F. Spill, A. Torrielli, and H. Yamane) Drinfeld second realization of the quantum affine superalgebras of D⁽¹⁾(2,1;x) via the Weyl groupoid
  In: RIMS Kôkyûroku Bessatsu B8 (2008), 171-216
• (with S. Kolb) Differential forms via the Bernstein-Gelfand-Gelfand resolution for quantized irreducible flag manifolds
  J. Geom. Phys. 57 (2007), no. 11, 2316-2344.
• (with H. Yamane) A generalization of Coxeter groups, root systems, and Matsumoto's theorem
  Math. Z. 259 (2008) 255-276
• (with M. Graña) On a factorization of graded Hopf algebras using Lyndon words
  J. Algebra 314 (2007) 324-343
• Classification of arithmetic root systems
  Adv. Math. 220 (2009) 59-124
• (with S. Kolb) On the Bernstein-Gelfand-Gelfand resolution for Kac-Moody algebras and quantized enveloping algebras
  Transform. Groups 12 (2007), no. 4, 647-655
• Nichols algebras of diagonal type and arithmetic root systems
  Habilitation thesis, Leipzig, December 2005
• (with A. Joseph) On the left and right BK-filtration
  Preprint, Weizmann Institute, June 2006
• Classification of arithmetic root systems of rank 3
  In: Actas del "XVI Coloquio Latinoamericano de Álgebra" (Colonia, Uruguay, 2005), 227-252
• Rank 2 Nichols algebras with finite arithmetic root system
  Algebr. Represent. Theor. 11 (2008) 115-132
• Weyl equivalence for rank 2 Nichols algebras of diagonal type
  In: Ann. Univ. Ferrara - Sez. VII - Sc. Mat., Vol. LI, pp. 281-289 (2005)
• The Weyl groupoid of a Nichols algebra of diagonal type
  Invent. Math. 164 (2006) 175-188
• Examples of finite dimensional rank 2 Nichols algebras of diagonal type
  Compositio Math. 143 (2007) 165-190
• Finite Dimensional Rank 2 Nichols Algebras of Diagonal Type II: Classification
  Preprint, April 2004. Will not be published. For similar results see the above paper Rank 2 Nichols algebras ...
• (with S. Kolb) De Rham Complex for Quantized Irreducible Flag Manifolds
  J. Algebra 305 (2006) 704-741
• (with S. Kolb) The Locally Finite Part of the Dual Coalgebra of Quantized Irreducible Flag Manifolds
  Proc. London Math. Soc. 89 (2004) 457-484
• (with S. Kolb) Differential Calculus on Quantum Homogeneous Spaces
  Lett. Math. Phys. 63 (2003) 255-264
• (with S. Kolb) Podles' Quantum Sphere: Dual Coalgebra and Classification of Covariant First Order Differential Calculus
  J. Algebra 263 (2003) 193-214
• (with S. Kolb) Differential Calculus on Quantum Complex Grassmann Manifolds II: Classification
  Unpublished preprint, December 2001
• Spin Geometry on Quantum Groups via Covariant Differential Calculi
  Adv. Math. 175 (2003) 197-242
• (with A. Schüler) Laplace operator and Hodge decomposition for quantum groups and quantum spaces
  Czech. J. Phys. 51 (2001) 1342-1347
• (with A. Schüler) De Rham Cohomology and Hodge Decomposition for Quantum Groups
  Proc. London Math. Soc. 83(3) (2001) 743-768
• Classification of Left-Covariant Differential Calculi on the Quantum Group SL_q(2)
  Journal of Algebra 237 (2001) 203-237
• (with A. Schüler) On FRT-Clifford algebras
  Adv. Appl. Clifford Algebras 10 (2000) 267-296
• (with A. Schüler) Symmetrizer and Antisymmetrizer of the Birman-Wenzl-Murakami Algebras
  Lett. Math. Phys. 50 (1999) 45-51
• Hodge and Laplace-Beltrami Operators for Bicovariant Differential Calculi on Quantum Groups
  Compositio Math. 123 (2000) 329-354
• (with A. Schüler) Exterior Algebras Related to the Quantum Group O(O_q(3))
  Czech. J. Phys. 48 (1998) 1355-1362
• Bikovariante Differentialkalküle erster Ordnung und Levi-Civita-Zusammenhünge auf Quantengruppen
  PhD thesis, Leipzig, October 1998
• (with K. Schmüdgen) Classification of Bicovariant Differential Calculi on the Quantum Groups SL_q(n+1) and Sp_q(2n)
  J. reine angew. Math. 502 (1998) 141-162
• (with A. Schüler) Higher Order Differential Calculus on SL_q(N)
  Czech. J. Phys. 47 (1997) 1153-1161
• (with K. Schmüdgen) Bicovariant Differential Calculi on SL_q(N) and Sp_q(N)
  Czech. J. Phys. 47 (1997) 1145-1151
• (with K. Schmüdgen) Levi-Civita Connections on the Quantum Groups SL_q(N), O_q(N) and Sp_q(N)
  Comm. Math. Phys. 185 (1997) 177-196
• Darstellungen von Quantengruppen bei Einheitswurzeln.
  Diploma thesis, Leipzig, 1993