Tadao Tannaka

Tadao Tannaka (Japanese淡 中 忠 郎, Tannaka Tadao; * December 27, 1908 in Matsuyama, Ehime Prefecture, Japan, † October 25, 1986 in Tokyo ) was a Japanese mathematician.

Tannaka made ​​1932 his bachelor's degree at the Imperial University of Tohoku, which later became Tohoku University. In 1934 he became a lecturer there in 1942 assistant professor and in 1945 professor. In 1941 he earned his doctorate at Tohoku University. In 1972 he retired there and then until 1981 was professor at Tohoku Gakuin University. 1955/57 he was at the Institute for Advanced Study and in 1955 he was one of the organizers of the International Symposium on Algebraic Number Theory in Tokyo and Nikko, in which there were also momentous contacts between André Weil and Japanese number theorists such as Goro Shimura and Yutaka Taniyama. He was also a long standing member of the Steering Committee of Japanese Mathematical Society and co-editor of the Tōhoku sūgaku zasshi (English Tohoku Mathematical Journal ).

He dealt mainly with algebraic number theory and proved, for example, generalizations of the principal ideal theorem of class field theory. After Tannaka several concepts are named ( Tannaka category, Tannaka - Krein duality or Tannaka - duality ). They have their origin in the work of Tannaka 1939, in which he examined how a compact ( non-commutative ) group from the set of its representations can be reconstructed, which is described in the commutative case, by the duality theorem of Pontryagin (reconstruction of an abelian group from the group of their characters ). In the West, was taken up, for example, by Claude Chevalley in the 1940s. Applying the concepts found in the formulation of the category theory in algebraic geometry the school of Alexander Grothendieck and his theory of motives in the 1960s and in the 1990s in the theory of quantum groups.