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We generalize the decomposition of $U_q(mathfrak g)$ introduced by A. Joseph and relate it, for $mathfrak g$ semisimple, to the celebrated computation of central elements due to V. Drinfeld. In that case we construct a natural basis in the center of $U_q(mathfrak g)$ whose elements behave as Schur polynomials and thus explicitly identify the center with the ring of symmetric functions.
In this paper we study the isotypic decomposition of the regular module of a finite-dimensional Hopf algebra over an algebraically closed field of characteristic zero. For a semisimple Hopf algebra, the idempotents realizing the isotypic decompositio
The aim of this paper is to generalize the classical formula $e^xye^{-x}=sumlimits_{kge 0} frac{1}{k!} (ad~x)^k(y)$ by replacing $e^x$ with any formal power series $displaystyle {f(x)=1+sum_{kge 1} a_kx^k}$. We also obtain combinatorial applications
One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra. A Lie pseudoalgebra is a generalization of the notion of a Lie co
In the present paper we introduce a quantum analogue of the classical folding of a simply-laced Lie algebra g to the non-simply-laced algebra g^sigma along a Dynkin diagram automorphism sigma of g For each quantum folding we replace g^sigma by its La
We begin a study of the representation theory of quantum continuous $mathfrak{gl}_infty$, which we denote by $mathcal E$. This algebra depends on two parameters and is a deformed version of the enveloping algebra of the Lie algebra of difference oper