Publications
Almost all publications are linked to a corresponding preprint.
For the final version (if any) please consult the publishing journal.
- (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 SLq(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(Oq(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 SLq(n+1) and
Spq(2n)
J. reine angew. Math. 502 (1998) 141-162
-
(with A. Schüler)
Higher Order Differential Calculus on SLq(N)
Czech. J. Phys. 47 (1997) 1153-1161
-
(with K. Schmüdgen)
Bicovariant Differential Calculi on SLq(N)
and Spq(N)
Czech. J. Phys. 47 (1997) 1145-1151
-
(with K. Schmüdgen)
Levi-Civita Connections on the Quantum Groups
SLq(N), Oq(N) and
Spq(N)
Comm. Math. Phys. 185 (1997) 177-196
-
Darstellungen von Quantengruppen bei Einheitswurzeln.
Diploma thesis, Leipzig, 1993
I. Heckenberger, Oct. 29, 2008