Igor Dmitrievich Ado (
Russian: Игорь Дмитриевич Адо, scientific
transliteration
Transliteration is a type of conversion of a text from one script to another that involves swapping letters (thus '' trans-'' + '' liter-'') in predictable ways, such as Greek → and → the digraph , Cyrillic → , Armenian → or L ...
''Igor' Dmitrievič Ado''; January 17, 1910 in
Kazan
Kazan; , IPA: Help:IPA/Tatar, ɑzanis the largest city and capital city, capital of Tatarstan, Russia. The city lies at the confluence of the Volga and the Kazanka (river), Kazanka Rivers, covering an area of , with a population of over 1. ...
June 30, 1983) was a Soviet mathematician. He was born into the family of a state employee and he lived in Kazan till the end of his life. After leaving school he entered the faculty of mathematics and physics at
Kazan State University, named after V. I. Lenin, from which he graduated in 1931. He was admitted to the PhD study at the Chair of Mathematics (since 1934 – Chair of Algebra) under the supervision of
Nikolai Chebotaryov. Igor Ado finished his PhD study by preparing a scientific qualifying work for the degree of a Candidate (PhD) of physical and mathematical sciences. The University board awarded him for this work the degree of
Doctor nauk (doctor of sciences) of physic-mathematical sciences. This is an analogue to the European
Habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...
and is very unusual to receive for a PhD work.
Igor Ado solved in his thesis a current problem of modern
abstract algebra
In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are set (mathematics), sets with specific operation (mathematics), operations acting on their elements. Algebraic structur ...
connected to representation theory of Lie algebras and
Lie group
In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable.
A manifold is a space that locally resembles Eucli ...
s. More precisely, he obtained the result which is now known as
Ado's Theorem In abstract algebra, Ado's theorem is a theorem characterizing finite-dimensional Lie algebras.
Statement
Ado's theorem states that every finite-dimensional Lie algebra ''L'' over a field ''K'' of characteristic zero can be viewed as a Lie algeb ...
: every finite-dimensional Lie algebra over a field of characteristic zero has a faithful finite-dimensional linear representation.
After the defense of his doctoral thesis Igor Ado started to work at Kazan State University. From 1936 till 1942 he held the position of professor at the Chair of Algebra. In 1942 Igor Ado moved to the Kazan State Chemical Technological Institute named after S.M. Kirov, now called
Kazan National Research Technological University where he held the Chair of High Mathematics until his death. He held the position of professor from 1942 to 1958 and from 1970 to 1983. During the period from 1958 to 1970 he was the head of the chair.
Igor Ado has 12 publications. He did research in group theory and representation theory. His most famous publication is the paper ''The representation of Lie algebras by matrices''.
Ado's Theorem has attracted the attention of many famous mathematicians who tried to improve its proof.
Kenkichi Iwasawa proved the theorem over a field of prime characteristic. For this reason Ado's Theorem is also called ''Ado-Iwasawa Theorem''. Many generalizations and refinements of Ado's Theorem have been considered.
References
External links
Словари и энциклопедии на Академике: Igor Dmitrijewitsch Ado(Russian)
Information of the Kazan State University on Igor Dmitrjevich Ado(Russian)
{{DEFAULTSORT:Ado, Igor
1910 births
1983 deaths
Soviet mathematicians