Before asking the question I should say that I don't know much about algebraic groups and I'm not sure if the question has the right level for MO. If not, please let me know and I will delete the question that emerged when I was trying to understand some theorems in a paper on the vanishing range of the cohomology of finite groups of Lie type.

Call an algebraic group (over an algebraically closed field) *simple* if it is simple as an abstract group and *almost simple* if it has finite center. Every almost simple algebraic group is of one of the following types:

$$A_n, B_n, C_n, D_n, E_6, E_7, E_8, F_4, G_2$$

**Question:** What are the simply connected simple algebraic groups (over an alg. closed field with no assumption on the characteristic) and of which type are they ?

*Counter-examples:* $SL_{n+1}$ is simply conntected almost simple of type $A_n$, but not simple while $PSL_{n+1}$ is simple but not simply connected of the same type.

**Added:** The mathematical problem is solved by Jay's answer. But I'm still confused about the terminology: In contrast to finite groups, where each simple group has a definite name, simple algebraic groups doesn't seem to have a name on their own (apart from the classical types). For example, by comments of Yves Cornulier and Jim Humphreys, for each type there is a unique simply connected simple alg. group. In my opinion it would be reasonable to give them a special name, for example $E_6^{sc}$. However the typical wording in the literature is like "let $G$ be a simply connected, connected complex algebraic group of type $E_6$".

Is there a particular reason for this convention ?