Abstract
This work studies three families of Hopf algebra Hq, H'q, Hʺq, each parametrized by a complex number q. The family Hq is related to the Hopf algebra of symmetric functions, H'q is a q-deformation of the tensor Hopf algebra T(V), H"q is the q-shuffle algebra of T(W). We prove that for q not in a certain subset of algebraic integers, Hq, H'q, H"q are isomorphic.
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