Classical and exceptional root systems and quantizations (Q941638)

The author presents a method for quantizing semisimple Lie algebras. The previous work of the author [``Braided symmetric and exterior algebras and quantizations of braided Lie algebras'', Russ. Math. 52, No. 4 (2008); translation from Izv. Vyssh. Uchebn. Zaved. Mat. 2008, No. 4, 73--84 (2008)] was devoted to quantizations of the braided Lie algebra structure on a finite dimensional graded vector space \(V\) by quantizations of braided derivations on the exterior algebra of \(V^*\). Now the author finds quantizations of semisimple Lie algebras using the grading by their roots. The paper goes through all root systems, classical and exceptional.