Zongzhu Lin, Kansas State University

Title: Free Tree algebras arising from Rota-Baxter extensions.

Abstract:  V. Jone's used subfactors constructed a towers of algebras, which turned out to closed related to Heck algebras and lead to the discovery of Jone's polynomials. We mimic the construction for Rota-Baxter extensions to construct a tower of  finite dimensional algebras. This turns out to be a deformation of free-tree monoid algebra considered by  A. Ayyer, A. Schilling, B. Steinberg, N. Thi´ery in their study of Morkov chains of $R$-trivial monoids. The additional parameters help to describe certain combinatorial properties of basis in terms of plane diagrams in the analogous fock space, in the same manner as partitions (young diagrams) are used to in computations of basis of fock spaces.