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Macquarie University  Department of Mathematics

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Categories in Algebra, Geometry and Mathematical Physics

Conference in honour of Ross Street's sixtieth birthday

July 11-16 2005, Macquarie University, Sydney

Wed, 13 July:  9:45 - 10:25

Generalized bialgebras and triples of operads
Loday, Jean-Louis (Université de Strasbourg)

The classical Poincaré--Birkhoff--Witt theorem and Cartier--Milnor--Moore theorem can be viewed as a rigidity result on cocommutative Hopf algebras intertwining the operads Com, As, and Lie of commutative algebras, associative algebras and Lie algebras respectively. Recently, in joint work with M. Ronco, we proved a similar rigidity result intertwining the operads As, 2as, and $B$-infinity, where 2as is the operad of algebras with 2 associative operations. We will present a general program aimed at discovering rigidity results for triples of operads $(C,A,P)$, where $C$ (resp.\ $A$, resp.\ $P$) is the operad governing the coalgebra structure (resp.\ the algebra strucutre, resp.\ the primitives).

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