Research:
- Hopf algebras and quantum
groups, primitive elements, noncommutative geometry, non-associative
algebras
- Operads, trees and related
methods (renormalization, Runge-Kutta)
- Formal groups, completions,
power series, algebraic cryptography, computer algebra, normal forms
(term-rewriting, Gröbner bases)
Links:
Reviews:
Publications:
-
Rooted trees appearing in products and co-products. In: Combinatorics and Physics,
Contemporary Mathematics 539, Amer. Math. Soc. (2011), 153-169.
(pdf)
- Planar trees, free
nonassociative algebras, invariants, and elliptic integrals. Joint with
V. Drensky. Algebra and Discrete Mathematics 2008, No.2, 1-41. MR2009k:17009 (=abstract) Zbl
1164.17009 (=abstract) (math.RA 0710.0493)
- Partial
magmatic bialgebras. Joint with E. Burgunder. Homology, Homotopy and
Applications 10 (2008), No.2, 59-81. MR2009e:18017 Zbl
1191.16034 (=abstract) (MPIM2007-93
/ math.RA 0708.4191 / HHA/v10/n2/a3)
- Ralf
Holtkamp, Jean-Louis Loday, Maria Ronco: "Coassociative magmatic
bialgebras and the Fine numbers", Journal of Algebraic Combinatorics 28
(2008), 97-114. MR2009f:16068 Zbl
1175.16027 (math.RA/0609125)
- On
Hopf algebra structures over free operads, Advances in Mathematics 207
(2006), 544-565. MR2007h:18012 Zbl
1117.16027 (abstract math.RA/0504531)
- Constants
of formal derivatives of non-associative algebras, Taylor expansions
and applications. Joint with V. Drensky. Rendiconti del Circolo
Matematico di Palermo (2), Vol.55 (2006), 369-384. MR2008g:17006 Zbl
1117.17002 (math.RA/0312082)
- Hopf
co-addition for free magma algebras and the non-associative Hausdorff
series. Joint with L. Gerritzen. Journal of
Algebra 265 (2003), 264-284. MR2004d:17002 Zbl
1046.17001 (abstract
math.RA/0207083)
- Comparison
of Hopf algebras on trees. Archiv der Mathematik,
Vol.80 (2003), 368-383. MR2004f:16067 Zbl1056.16030 (abstract - html)
- (Contribution)
Spectral Triples and Abstract YM Functional. In: NCG and the Standard
Model of Elementary Particle Physics (Eds. F. Scheck, H. Upmeier, W.
Werner), Lecture
Notes in Physics 596 (2002). MR2004k:58045
Zbl
1042.81103
- A
Pseudo-Analyzer Approach to Formal Group Laws not of Operad Type.
Journal of Algebra 237 (2001), 382-405. MR2002h:14074 Zbl
1042.14020=(abstract-
html)
- On
formal quantum group laws. Archiv der Mathematik, Vol.73, Nr.2 (1999),
90-103. MR2000i:16085
Zbl
0935.16026 (abstract-
txt)
- On
Gröbner bases of noncommutative power series. Joint
with L. Gerritzen. Indagationes Mathematicae,
New Series Vol.9, No.4 (1998), 503-519. MR2000c:16035 Zbl
0930.16017 (abstract- txt) / (introd.talk
on same subject - ps)
- On quantum general linear groups.Joint
with L. Gerritzen. Indagationes Mathematicae,
New Series Vol.8, No.1 (1997), 43-54. MR99e:17019
Zbl
0888.16019 (abstract
- txt)
Dissertation:
Zur
Theorie der formellen Quantengruppen, Ruhr-Univ.Bochum (1997).
Habilitation:
On Hopf algebra
structures over operads, Ruhr-Univ.Bochum (2004). (math.RA/0407074)