nLab Mitsuhiro Takeuchi

Mitsuhiro Takeuchi is a Japanese algebraist. Much of his work is dedicated to bialgebras, Hopf algebras, coalgebras, (co)module algebras, Hopf-Galois extensions and various generalizations of these concepts as well as applications of bialgebras to the theory of algebraic and formal groups and quotients.

Selected writings

On the Gabriel-Popescu theorem:

• Mitsuhiro Takeuchi: A simple proof of Gabriel and Popesco’s theorem, J. Alg. 18 (1971) 112-113 (1971) [doi:10.1016/0021-8693(71)90130-X]

On Hopf algebras and Galois extensions:

• H. F. Kreimer, M. Takeuchi, Hopf algebras and Galois extensions of an algebra, Indiana Univ. Math. J. 30 (1981), 615-692 web pdf djvu

On Morita equivalence induce by bimodules over Hopf-Galois extensions:

• Stefaan Caenepeel, Septimiu Crivei, Andrei Marcus, Mitsuhiro Takeuchi, Morita equivalences induced by bimodules over Hopf–Galois extensions, J. Algebra 314 (2007) 267–302 pdf

• Y. Doi, Mitsuhiro Takeuchi, Cleft comodule algebras for a bialgebra, Comm. Alg. 14 (1986) 801–818 doi

• M. Takeuchi, Matched pairs of groups and bismash products of Hopf algebras, Comm. Alg. 9:8 (1981) 841–882 doi

Introducing the left adjoint to the forgetful functor from Hopf algebras to coalgebras and (by composing) also to the forgetful functor to vector spaces (the free Hopf algebra functor), together with a first example of a Hopf algebra with non-bijective antipode:

• Mitsuhiro Takeuchi: Free Hopf algebras generated by coalgebras, J. Math. Soc. Japan 23:4 (1971) 561–582

Introducing what came to be called the Takeuchi product of $A$-rings (where $A$ is a noncommutative ring):

• Mitsuhiro Takeuchi: Groups of algebras over $A \times \bar{A}$, J. Math. Soc. Japan 29, 459–492, 1977, MR0506407, euclid

  Beware that the terminology of ends vs coends here is swapped as compared to, say, MacLane’s CWM.

category: people