  The $(q,t)$-Cartan matrix specialized at $t=1$, usually called the quantum
Cartan matrix, has deep connections with (i) the representation theory of its
untwisted quantum affine algebra, and (ii) quantum unipotent coordinate
algebra, root system and quantum cluster algebra of kew-symmetric type. In this
paper, we study the $(q,t)$-Cartan matrix specialized at $q=1$, called the
$t$-quantized Cartan matrix, and investigate the relations with (ii') its
corresponding quantum unipotent coordinate algebra, root system and quantum
cluster algebra of skew-symmetrizable type.
