Keynes understood that central banks could push rates on short-term government debt to zero. The liquidity trap, as Keynes used the term, is better thought of as a term-structure trap or, more generally, a limit on how low long-term and private interest rates can go once the interest rate on short-term government debt is  BIS Review 110/1999  4  pushed to zero.
When short-term government rates reached zero, Keynes believed that there would still be positive interest rates on both longer-term government securities and private debt and that monetary policy then would be unable to push those rates any lower. The conventional view is that the level of long-term rates is determined by current and expected shortterm rates.