Quantum Algebras with Representation Ring of % Mathtype!Mtef!2!1!+- % Feaafiart1Ev1Aaatcvaufebsjuyzl2Yd9Gzlbvynv2Caerbulwbln % Hiov2Dgi1Btfmbaexatlxbi9Gbaerbd9Wdylwzybitldharqqtubsr % 4Rnchbgeagqivu0Je9Sqqrpepc0Xbbl8F4Rqqrffpeea0Xe9Lq-Jc9 % Vqaqpepm0Xbba9Pwe9Q8Fs0-Yqaqpepae9Pg0Firpepekkfr0Xfr-X % Fr-Xb9Adbaqaaegacigaaiaabeqaamaabaabaagcbawefv3Yslgzgj % Xyrrxdybqeguudjxwakbiryf2A0Vncagqbaiab-Xc8Zjab-Vc8Snaa % Baaaleaacgas0Homaaqabaaaaa!46Dc! $$ \Mathfrak{S}\Mathfrak{L}_2 $$ Type