His use of the Yang-Baxter equation led to the formulation and the study of representations of the quantum group by Vladimir Drinfeld in the 1980s, and quantum generalizations of affine algebras, and they are quasi-triangular Hopf algebras which yield solutions of the Yang-Baxter equation and provide insight into the properties of corresponding statistical models.
Drinfeld introduced the notion of a quantum group (independently discovered by Michio Jimbo at the same time) and made important contributions to mathematical physics, including the ADHM construction of instantons, algebraic formalism of the Quantum inverse scattering method, and the Drinfeld–Sokolov reduction in the theory of solitons.
Vladimir Putin | Vladimir Lenin | Vladimir Nabokov | Vladimir Ashkenazy | Vladimir Horowitz | Vladimir | Vladimir Jurowski | Order of St. Vladimir | Vladimir Spivakov | Vladimir Bukovsky | Vladimir Vysotsky | Vladimir Mayakovsky | Vladimir Feltsman | Vladimir Oblast | Vladimir Kramnik | Vladimir Rosing | Vladimir Nasedkin | Vladimir Romanov | Vladimir Popovkin | Vladimir Solovyov | Vladimir Shukhov | Vladimir Minorsky | Vladimir Drinfeld | Vladimir Bortko | Vladimir Zhirinovsky | Vladimir Vazov | Vladimir Krantz | Vladimir Guerrero | Vladimir Grinin | Vladimir Fock |
Manin had over 40 doctoral students, including Vladimir Berkovich, Mariusz Wodzicki, Alexander Beilinson, Ivan Cherednik, Alexei Skorobogatov, Vladimir Drinfeld, Vyacheslav Shokurov, Arend Bayer and Victor Kolyvagin, as well as foreign students including Hà Huy Khoái, now the most senior mathematician in Vietnam.