(25 December 1927 – 10 October 2014) was a Japanese mathematician working on

algebraic group In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Man ...

s who introduced the

Satake isomorphism In mathematics, the Satake isomorphism, introduced by , identifies the Hecke algebra of a reductive group over a local field with a ring of invariants of the Weyl group. The geometric Satake equivalence is a geometric version of the Satake isomorph ...

and

Satake diagram In the mathematical study of Lie algebras and Lie groups, a Satake diagram is a generalization of a Dynkin diagram introduced by whose configurations classify simple Lie algebras over the field of real numbers. The Satake diagrams associated to a D ...

s. He was considered an iconic figure in the theory of

linear algebraic group In mathematics, a linear algebraic group is a subgroup of the group of invertible n\times n matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation M^TM = I_n wh ...

s and symmetric spaces. Satake was born in

Tokyo, Japan Tokyo (; ja, 東京, , ), officially the Tokyo Metropolis ( ja, 東京都, label=none, ), is the capital and List of cities in Japan, largest city of Japan. Formerly known as Edo, its metropolitan area () is the most populous in the world, ...

in 1927, and received his Ph.D. at the

University of Tokyo , abbreviated as or UTokyo, is a public research university located in Bunkyō, Tokyo, Japan. Established in 1877, the university was the first Imperial University and is currently a Top Type university of the Top Global University Project by ...

in 1959 under the supervision of

Shokichi Iyanaga was a Japanese mathematician. Early life Iyanaga was born in Tokyo, Japan on April 2, 1906. He studied at the University of Tokyo from 1926 to 1929. He studied under Teiji Takagi. As an undergraduate, he published two papers in the ''Japanese ...

. He was a professor at

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

from 1968 to 1983. After retirement he returned to Japan, where he spent time at

Tohoku University , or is a Japanese national university located in Sendai, Miyagi in the Tōhoku Region, Japan. It is informally referred to as . Established in 1907, it was the third Imperial University in Japan and among the first three Designated National ...

and

Chuo University , commonly referred to as or , is a private flagship research university in Tokyo, Japan. Founded in 1885 as Igirisu Hōritsu Gakkō (the English Law School), Chuo is one of the oldest and most prestigious institutions in the country. The univer ...

. He died of

respiratory failure Respiratory failure results from inadequate gas exchange by the respiratory system, meaning that the arterial oxygen, carbon dioxide, or both cannot be kept at normal levels. A drop in the oxygen carried in the blood is known as hypoxemia; a rise ...

on 10 October 2014. Although they are often attributed to

William Thurston William Paul Thurston (October 30, 1946August 21, 2012) was an American mathematician. He was a pioneer in the field of low-dimensional topology and was awarded the Fields Medal in 1982 for his contributions to the study of 3-manifolds. Thurston ...

, Satake was the first to introduce

orbifold In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold. Roughly speaking, an orbifold is a topological space which is locally a finite group quotient of a Euclidean space. D ...

, which he did in the 1950s under the name of ''V-manifold''. In , he gave the modern definition, along with the basic calculus of smooth functions and

differential form In mathematics, differential forms provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds. The modern notion of differential forms was pioneered by Élie Cartan. It has many applications, ...

s. He demonstrated that the

de Rham theorem In mathematics, de Rham cohomology (named after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable of expressing basic topological information about smooth manifolds in a form particularly adapte ...

and

Poincaré duality In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds. It states that if ''M'' is an ''n''-dimensional oriented closed manifold (compact a ...

, along with their proofs, carry over to the orbifold setting. In , he demonstrated that the standard

tensor calculus In mathematics, tensor calculus, tensor analysis, or Ricci calculus is an extension of vector calculus to tensor fields (tensors that may vary over a manifold, e.g. in spacetime). Developed by Gregorio Ricci-Curbastro and his student Tullio Levi ...

of bundles, connections, and curvature also carries over to orbifolds, along with the Chern-Gauss-Bonnet theorem and

Shiing-Shen Chern Shiing-Shen Chern (; , ; October 28, 1911 – December 3, 2004) was a Chinese-American mathematician and poet. He made fundamental contributions to differential geometry and topology. He has been called the "father of modern differential geome ...

's proof thereof.Shiing-shen Chern. ''A simple intrinsic proof of the Gauss-Bonnet formula for closed Riemannian manifolds.'' Ann. of Math. (2) 45 (1944), 747–752.

Major publications

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References

External links

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FORMULA IN SIMPLE JORDAN ALGEBRAS ICHIRO SATAKE (Received May 7, 1984)
{{DEFAULTSORT:Satake, Ichiro 1927 births 2014 deaths Deaths from respiratory failure 20th-century Japanese mathematicians 21st-century Japanese mathematicians University of California, Berkeley faculty University of Tokyo alumni Tohoku University faculty Chuo University faculty University of Chicago faculty People from Tokyo Group theorists Topologists