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The fact that α is a morphism of lax monoidal functors is the same as (6.4) and the coassociativity of I in (6.8). The fact that λ and ρ are morphisms of lax functors is the same as (6.6) and the c...
Let A be a Hopf algebra over a field K of characteristic zero such that its coradical H is a finite dimensional sub-Hopf algebra. Our main theorem shows that there is a gauge transformation  on A suc...
In this paper we use the technique of Hopf algebras and quasi-symmetric functions to study the combinatorial polytopes. Consider the free abelian group $\mathcal{P}$ generated by all combinatorial po...
Let G be a finite group, (g_{1},...,g_{r}) an (unordered) r-tuple of G^{(r)} and x_{i,g_i}'s variables that correspond to the g_i's, i=1,...,r. Let F be the corresponding free...
We obtain an analog of Shvedov theorem for convex multivariate approximation by algebras of continuous functions.
We study factorization and dilation properties of Markov maps between von Neumann algebras equipped with normal faithful states, i.e., completely positive unital maps which preserve the given states...

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