The electronic structure of YMnO3 in its high-and low-temperature hexagonal phases has been investigated within the local spin-density approximation (LSDA) and by the LSDA + U method which takes into account the local Coulomb interaction between d electrons of transition-metal ions. In contrast to the case for orthorhombic manganites, the d4-configuration degeneracy is already lifted in the high-temperature symmetric hexagonal phase, indicating that Mn3+ is not a Jahn-Teller ion; hence, we argue that the lowering of the symmetry is not connected with Jahn-Teller instability in hexagonal YMnO3. Each of these two hexagonal phases is found to be semiconducting, with a band gap of about 1.5 eV. It is shown that magnetism and correlation effects are important in band-gap formation for both crystal structures. Using the Green function method, we estimated the Neel temperature from the calculated effective exchange interaction parameters, and found it to be in good agreement with experiment.