GROUP BIALGEBRAS AND PERMUTATION BIALGEBRAS
GROUP BIALGEBRAS AND PERMUTATION BIALGEBRAS
Abstract Malvenuto and Reutenauer (C. Malvenuto and C. Reutenauer, Duality between quasi-symmetric functions and the Solomon descent algebra, J. Algebra 177 (1995), 967–982) showed how the total symmetric group ring ⊕ n Z Σ n could be made into a Hopf algebra with a very nice structure which admitted the …