Fachbereich Mathematik
FachbereichMathematik
Homepages
(hier geht es zur ggf. vollständigeren Homepage im alten Layout)
(this way to the possibly more complete Homepage in the old layout)
Habilitation: On Hopf algebra structures over operads, Ruhr-Univ.Bochum (2004). (math.RA/0407074)
(this way to the possibly more complete Homepage in the old layout)
Ralf Holtkamp
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)
Short CV (pdf), Lehre/Teaching
Links:
- Department Mathematik (UHH) - Ralf Holtkamp
- Max-Planck-Institut für Mathematik
- Math. Forschungsinstitut Oberwolfach
- Mathematical Sciences Research Institute
- Institut Mittag-Leffler
- Erwin Schrödinger International Institute
- Chern Institute of Mathematics
- C.I.R.M Luminy
Reviews:
- Reviewer for Mathematical 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)
Habilitation: On Hopf algebra structures over operads, Ruhr-Univ.Bochum (2004). (math.RA/0407074)