BICOVARIANT 3D CALCULUS FOR SL(Q)(2) FROM POISSON-LIE STRUCTURES

All possible graded Poisson-Lie structures on the external algebra of SL(2) are described. We prove that differential Poisson-Lie structures prolonging the Sklyanin brackets do not exist on SL(2). There are two and only two graded Poisson-Lie structures on SL(2) and neither of th em can be obtained by a reduction of graded Poisson-Lie structures on the external algebra of GL(2). Both of them can be quantized and as a result we get new graded algebras of quantum right-invariant forms on SL(q)(2) with three generators. (C) 1994 American Institute of Physics .