Lecture on "Algebras,
Operads, Combinads" (exposé à Lille le 23 mars 2012) Abstract. A type of
algebras is encoded by an operad. Similarly a type of operads is
encoded by a combinad. We
describe what is a combinad, and give some details on two examples:
nonsymmetric operads and permutads. We introduce circled trees and
higher operadic structures which look like opetopes. We exhibit an
attractive relationship with the canonical basis of quantum groups as
introduced by G. Lusztig and M. Kashiwara.
"Dichotomy
of
the
addition
of
natural
numbers", in "Associahedra,
Tamari Lattices and Related Structures", Tamari Memorial
Festschrift,
F. Mueller-Hoissen, J. Pallo and J. Stasheff (Eds.), Progress in
Mathematics, vol. 299, Birkhauser, 2012.
"Some
problems in operad theory", Proc. Int. Conf., in Nankai
Series in Pure, Applied Mathematics and Theoretical Physics, Vol. 9
(World Scientific, Singapore, 2012), 139--146.
"Combinatorial
Hopf
Algebras" with
Maria Ronco, Quanta of maths, 347–383, Clay Math. Proc., 11,
Amer. Math. Soc., Providence, RI, 2010.
"The diagonal of
the
Stasheff polytope", Higher structures in
geometry and physics, 269–292, Progr. Math., 287,
Birkhäuser/Springer, New York, 2011.
arXiv:0710.0572
"Cyclic homology theory"
with M. Wodzicki, Lecture notes on noncommutative geometry and quantum
groups, European Mathematical Society Publishing House, ed. Piotr M.
Hajac, to appear. pdf
G.W. Zinbiel, Encyclopedia
of
types
of
algebras
2010, Proc.
Int. Conf., in Nankai Series in Pure, Applied Mathematics and
Theoretical Physics, Vol. 9 (World Scientific, Singapore, 2012),
217--298.
Dernières modifications / Last modifications : Mar 2012
