* African and European heads of state and government meet for summit
* Fourth summit aims to promote peace, jobs, investment
* EU commits to peacekeeping force for Central African Republic
* Zimbabwe's Mugabe, South Africa's Zuma decide to stay away
By Luke Baker
BRUSSELS, April 2 (Reuters) - Presidents and prime ministers from Europe and Africa gathered in Brussels on Wednesday for an EU-Africa summit designed to promote peace and investment on the world's poorest continent.
But cracks emerged even before the conference got underway, with some African leaders, including Zimbabwe's Robert Mugabe and South Africa's Jacob Zuma, deciding not to attend following a dispute over the invitation list.
Mugabe, now 90 and the president of Zimbabwe since 1987, stayed away because his wife, Grace, was not invited.
Both Mugabe and his wife are subject to travel bans under EU sanctions following the government's crackdown on political opponents, but the European Union routinely waives those restrictions to allow Mugage to attend international meetings.
In this case, EU officials said Grace had not been invited because no spouses were attending the summit, which already counts 65 heads of state and government and around 20 secretaries-general, including United Nations head Ban Ki-moon.
Following Mugabe's protest, South Africa's Zuma also decided to stay at home, sending his foreign minister instead.
Initially that was said to have been due to political considerations, with elections coming up in a month. But Zuma was later quoted by the South African Broadcasting Service as saying he did not like the way the summit had been set up.
"I think that time must pass wherein we are looked at as subjects, we are told who must come and who must not come," he said. "I thought the African Union and the European Union are equal organisations representing two continents, but there is not a single one of them who must decide for others."
The centre of Brussels, a city accustomed to summits since the EU's 28 leaders meet every few months, was shut down almost entirely for the arrival of the African heads of state, with heavily guarded motorcades charging through the town.
European Council President Herman Van Rompuy, who has visited several African countries to prepare for the summit, described the occasion as an opportunity to discuss how to move beyond Europe's colonial past and tackle the challenges of peace, security, growth and jobs in Africa.
"The theme we have chosen addresses the everyday concerns of our citizens - their safety and security, their job prospects and their future as families and individuals," he said.
The European Union is far and away Africa's biggest development partner, providing more than 140 billion euros in aid between 2007 and 2013, including 18 billion in 2012 - nearly half the world's aid to the continent.
But the point of the summit is to try to move beyond emergency or development help and build "partnerships" in areas such as health, education, energy, agriculture, climate change and issues such as democracy and human rights.
At the same time, the EU this week formally committed forces to a peacekeeping operation in the Central African Republic, a reminder that peace and stability are a pre-requisite for any closer trade and investment relations.
(Writing by Luke Baker; Editing by Angus MacSwan)