Arkady Onishchik

Arkady Onishchik
Born
Arkady L'vovich Onishchik

(1933-11-14)14 November 1933
Moscow, Russian Federation, Soviet Union
Died12 February 2019(2019-02-12) (aged 85)
Moscow, Russia
Alma materMoscow State University
Known forMatsushima–Onishchik Theorem
AwardsMoscow Mathematical Society Prize (1962)
Scientific career
FieldsMathematics
InstitutionsMoscow State University
Yaroslavl State University
Doctoral advisorEugene Dynkin
Doctoral studentsMikhail Borovoi
Vera Serganova

Arkady L'vovich Onishchik (Russian: Арка́дий Льво́вич Они́щик, born 14 November 1933[1] in Moscow; died 12 February 2019[2]) was a prominent Soviet and Russian mathematician, who worked on Lie groups and their geometrical applications. Onishchik was a student of Eugene Dynkin,[3] under whose guidance he got his PhD at Moscow State University in 1960.[1] In 1962 Onishchik received the Prize of the Moscow Mathematical Society for young mathematicians.[4] In 1970 he got Habilitation (Russian title of Doctor of Sciences).[1] Since 1975 Onishchik was a professor of Yaroslavl State University.[2]

Onishchik introduced new homotopy invariants of homogeneous spaces and classified factorizations of connected simple compact Lie groups into the product of two connected Lie subgroups.[1] In complex analysis, the Matsushima–Onishchik theorem describes homogeneous spaces of complex reductive groups that are Stein manifolds.[1] In addition to Lie groups and algebras, Onishchik also worked on nonabelian cohomology and on supermanifolds.[2]

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. ^ a b c d e Arkadiĭ Lʹvovich Onishchik (on the occasion of his seventieth birthday)
  2. ^ a b c Arkady L'vovich Onishchik (obituary)
  3. ^ Arkady Onishchik at the Mathematics Genealogy Project
  4. ^ Laureates of the prize of the Moscow Mathematical Society

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).