Hi folks - I have a couple of basic questions about fundamental representations. First of all, does every group have a set of fundamental representations? Secondly, I know that in the case of the (compact?) semi-simple groups, any other representation of the group can be constructed by taking tensor products of its L fundamental representations, where L is the group's rank. Is this the case for all groups, or just the semi-simple ones? Any help would be really appreciated. Thanks!