What type of government was created by Oliver Cromwell after the civil war?
Cromwell helped create a republic (called the commonwealth) after the execution of Charles I in January 1649. From 1653 to his death in 1658, Cromwell ruled as Lord Protector of the British Commonwealth.
Establishing a republic meant there was no monarchy. This was a very radical move in that time period. The prevalent belief was that power on earth descended top down, from God in heaven through God's anointed king or queen. From there, power extended in greater chain of being, to the aristocracy and then to the people. A government derived from the will of the people seemed to many a violation of God's plan for the world. To some groups, such as the Quakers, the execution of the king signaled the Second Coming of Christ: with the monarch removed, the Quakers (and other radical religious sects) thought Christ was soon to arrive to rule the earth himself.
Instead, they got the military leadership of Oliver Cromwell.
Cromwell actually treated the dissenting religious groups with a higher level of tolerance than they had met with before the Civil War or would meet with for decades after the restoration on the monarchy. Cromwell did not want to rule as a military dictator and supported England's first-ever written constitution, The Instrument of Government. This document made the position of Lord Protector an elected position, rather than hereditary one, although the person so elected held the position for life.
Although Cromwell did not set out to make this happen, he ended up creating a dictatorship with himself as the head of the government. So you can say that the type of government he created was a dicatatorship.
What Cromwell really wanted, and what he first tried to set up, was a republic run by Parliament. However, for various reasons, this did not work out very well. Cromwell came to believe that he needed to take more and more control of the government. Eventually, what was left of Parliament after Cromwell got rid of his political enemies dissolved itself and gave all its powers to Cromwell. Cromwell also set up a system in which eleven of his generals ran the local governments around the country.
By doing these things, Cromwell set up what can best be described as a dictatorship.