Tadao Tannaka

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

Tannaka made his bachelor's degree in 1932 at the Imperial University of Tōhoku , the later University of Tōhoku. In 1934 he became a lecturer there, in 1942 assistant professor and in 1945 professor. In 1941 he received his doctorate from Tōhoku University. In 1972 he retired there and was then professor at Tōhoku Gakuin University until 1981 . In 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 Nikkō , during which there were significant contacts between André Weil and Japanese number theorists such as Gorō Shimura and Yutaka Taniyama . He was also a long-time member of the board of directors of the Japanese Mathematical Society and co-editor of Tōhoku sūgaku zasshi (English Tohoku Mathematical Journal ).

He was mainly concerned with algebraic number theory and proved as generalizations of the principal ideal theorem of class field theory . Several concepts are named after Tannaka (Tannaka category, Tannaka-Kerin duality or Tannaka duality). They have their origin in a work by Tannaka 1939, in which he investigated how a compact (non-commutative) group can be reconstructed from the set of its representations , which in the commutative case is described by Pontryagin's duality theorem (reconstruction of an Abelian group from the group of their characters). In the West, for example , this was picked up by Claude Chevalley in the 1940s. The concepts were applied in the formulation of the category theory in the algebraic geometry of the school of Alexander Grothendieck and his theory of motives in the 1960s and in the 1990s in the theory of quantum groups .

literature

• Obituary for Tannaka and photo in Tohoku Mathematical Journal, Vol. 39, 1987, No. 1
• Joyal, Street Introduction to Tannaka Duality and Quantum Groups , in Category Theory II, Proc. Como 1990 , Lecturesnotes in Mathematics, vol. 1488, 1991, p.411, PDF file

Individual evidence

1. ↑ Taniyama-Shimura conjecture , sometimes also called the Shimura-Taniyama-Weil conjecture
2. ↑ also sometimes after Mark Kerin named
3. ↑ On the duality theorem of non-commutative topological groups , Tohoku Math. J., Vol. 45, 1939, pp. 1-12
4. ^ Theory of Lie groups, 1946