  We classify the (semi-simple parts of the) Lie algebra of the Zariski closure
of a discrete subgroup of a split simple real-algebraic Lie group, whose limit
sets are minimal and such that the limit set in the space of full flags
contains a positive triple of flags (as in Lusztig). We then apply our result
to obtain a new proof of Guichard's classification of Zariski closures of
Hitchin representations into $PSL_d(\mathbb{R}).$
