Differential calculi on standard quantizations of simple algebraic groups

In the present paper differential calculi on quantum groups are studied, following S. L. Woronowisz. A non-existence of bicovariant differential calculi on the standard quantizations of simple algebraic groups is proved, ground field is taken to be $\mathcal K=k(q)$. Left-covariant differential calculus on $SL_q(2)$ is constructed and homology of algebra $U_q(sl(2))$ with coefficients in finite-dimensional modules is computed.