Abstract
Let U q + be the “upper triangular part” of the quantized enveloping algebra associated with a symetrizable Cartan matrix. We show that U q + is isomorphic (as a Hopf algebra) to the subalgebra generated by elements of degree 0 and 1 of the cotensor Hopf algebra associated with a suitable Hopf bimodule on the group algebra of Z n . This method gives supersymetric as well as multiparametric versions of U q + in a uniform way (for a suitable choice of the Hopf bimodule). We give a classification result about the Hopf algebras which can be obtained in this way, under a reasonable growth condition. We also show how the general formalism allows to reconstruct higher rank quantized enveloping algebras from U q sl(2) and a suitable irreducible finite dimensional representation.
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