Arkady L'vovich Onishchik (russian: link=no, Арка́дий Льво́вич Они́щик, born 14 November 1933Arkadiĭ Lʹvovich Onishchik (on the occasion of his seventieth birthday)
/ref> in Moscow; died 12 February 2019 Arkady L'vovich Onishchik (obituary)
/ref>) was a prominent Soviet and Russian mathematician, who worked on Lie groups and their geometrical applications. Onishchik was a student of Eugene Dynkin, under whose guidance he got his PhD at Moscow State University in 1960. In 1962 Onishchik received the Prize of the

Moscow Mathematical Society The Moscow Mathematical Society (MMS) is a society of Moscow mathematicians aimed at the development of mathematics in Russia. It was created in 1864, and Victor Vassiliev is the current president. History The first meeting of the society wa ...

for young mathematicians.Laureates of the prize of the Moscow Mathematical Society
/ref> In 1970 he got Habilitation ( Russian title of Doctor of Sciences). Since 1975 Onishchik was a professor of

Yaroslavl State University The Yaroslavl Demidov State University (Russian: ''Ярославский государственный университет имени П. Г. Демидова'') is an institution of higher education in Yaroslavl, Russia. In 1918, Yaroslav ...

. Onishchik introduced new

homotopy invariant In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from grc, ὁμός "same, similar" and "place") if one can be "continuously deformed" into the other, such a deforma ...

s of

homogeneous space In mathematics, particularly in the theories of Lie groups, algebraic groups and topological groups, a homogeneous space for a group ''G'' is a non-empty manifold or topological space ''X'' on which ''G'' acts transitively. The elements of ' ...

s and classified factorizations of connected simple compact

Lie group In mathematics, a Lie group (pronounced ) is a group that is also a differentiable manifold. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additio ...

s into the product of two connected Lie subgroups. In

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates Function (mathematics), functions of complex numbers. It is helpful in many branches of mathemati ...

, the Matsushima–Onishchik theorem describes homogeneous spaces of complex reductive groups that are Stein manifolds. In addition to Lie groups and algebras, Onishchik also worked on nonabelian cohomology and on supermanifolds.

Books

* with E. B. Vinberg: ''Lie groups and algebraic groups'', Springer-Verlag 1990. * ''Topology of transitive transformations groups.'' Barth, Leipzig 1994. * with E. B. Vinberg: (Eds.): ''Lie groups and Lie algebras.'' 3 volumes. Encyclopaedia of Mathematical Sciences, Springer-Verlag, of which by him: ** with E. B. Vinberg: ''Foundations of Lie theory,'' in Vol. 1, 1997. ** with V. V. Gorbatsevich: ''Lie transformation theory,'' in Vol. 1. ** with V. V. Gorbatsevich and E. B. Vinberg: ''Structure of Lie groups and Lie algebras,'' in Vol. 3, 1994. * ''Lectures on real semisimple Lie algebras and their representations.'' European Mathematical Society, Zürich 2004. * with Rolf Sulanke: ''Projective and Cayley-Klein Geometries.'' Springer-Verlag, 2006.

References

1. D. N. Akhiezer, È. B. Vinberg, V. V. Gorbatsevich, V. G. Durnev, R. Sulanke, L, S. Kazarin, D. A. Leites, V. V. Serganova, V. M. Tikhomirov. Arkadiĭ Lʹvovich Onishchik (on the occasion of his seventieth birthday). (Russian) Uspekhi Mat. Nauk 58 (2003), no. 6(354), 193–200 (DOI: https://doi.org/10.4213/rm695). English translation in Russian Math. Surveys 58 (2003), no. 6, 1245–1253 (DOI: http://dx.doi.org/10.1070/RM2003v058n06ABEH000695). 2. D. N. Akhiezer, È. B. Vinberg, V. V. Gorbatsevich, L. S. Kazarin, D. A. Leites, A. M. Lukatskii, A. N. Shchetinin. Arkady L'vovich Onishchik (obituary). (Russian) Uspekhi Mat. Nauk 75 (2020), no. 4(454), 195–206 (DOI: https://doi.org/10.4213/rm9941). English translation in Russian Math. Surveys 75 (2020), no. 4, 765–777 (DOI: http://dx.doi.org/10.1070/RM9941).

External links

Dynkin Collection

Mathnet.ru

Autor's profile Arkady L’vovich Onishchik at zbMATH
{{DEFAULTSORT:Onishchik, Arkady 1933 births 2019 deaths Russian mathematicians Moscow State University alumni Academic staff of Moscow State University Academic staff of Yaroslavl State University Scientists from Moscow