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Speaker:
Li Guo, Rutgers University at Newark
Title:
Free Rota-Baxter algebras, shuffle products,
rooted trees and operads
Abstract:
A Rota-Baxter algebra is an algebra with a
linear endomorphism P that satisfies the relation
P(x)P(y)=P(xP(y))+P(P(x)y)+lambda P(xy) for
all x, y.
Here lambda is a fixed constant. After a brief summary
of its basic properties and main applications, we will
focus on the construction of free Rota-Baxter
algebras. In the commutative case, the construction is
related to the shuffle product and quasi-shuffle
product with applications to multiple zeta values and
symmetric functions. In the noncommutative case, it is
related to planar rooted trees with decorations. As an
application, we study the adjoint functor of the
functor first found by Aguiar from Rota-Baxter
algebras to dendriform algebras.
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