Vladimir Vladimirovich Morozov

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Wladimir Wladimirowitsch Morosow ( Russian Владимир Владимирович Морозов , English transcription Vladimir Vladimirovich Morosov or Morozov ; * 1910 in Wologda ; † 1975 ) was a Russian mathematician who dealt with Lie groups and transformation groups .

Morozov, the son of a doctor, began in 1927 at the University of Kazan , where he researched and taught from 1930 and received his doctorate in 1938 under Nikolai Grigoryevich Chebotaryov . His first publication on transformation groups took place in 1930. That of Sophus Lie originating duck problem of classification of primitive transformation groups led him to the problem of classification maximal subgroups of Lie groups. He completed his habilitation in Kazan in 1943 (on non-semi-simple maximum subgroups of simple Lie groups). Eugene Dynkin also worked independently around 1950 on the classification of the maximal subgroups of semi-simple Lie groups. Morosow was from 1947 head of the algebra department in Kazan and from 1947 to 1953 dean of the faculty for mathematics and physics.

A theorem on nilpotent elements of semi-simple Lie algebras is named after him and Nathan Jacobson . It says that every such nilpotent element is part of a sub-algebra isomorphic to a sl2 Lie algebra. Morosow proved this as early as 1942. The 1942 essay also contains Borel and Morozov's theorem (all maximum solvable subalgebras of a semi-simple Lie algebra are conjugated), which he derives from the theorem of the nilpotent element. His proof for the theorem of the nilpotent element contained a loophole that Jacobson pointed out in 1951 (in 1960 Morozow published another correct proof of the theorem).

Further work concerned ordinary differential equations and the theory of resolvents (also a field of work of his teacher Chebotaryov).

literature

  • Biography in Transformation Groups, 15, 2010, pp. 743–750 (booklet dedicated to him)
  • Morosov On Primitive Groups (Russian), Mat. Sbornik, 5, 1939, 355-390
  • Morosov On the Centralizer of a Semi-Simple Sub-Algebra of a Semi-Simple Lie Algebra (Russian), Dokl. Akad. Nauka, 36, 1942, 259-261

Web links

Individual evidence

  1. ↑ Wladimir Wladimirowitsch Morosow in the Mathematics Genealogy Project (English)Template: MathGenealogyProject / Maintenance / id used
  2. ↑ On the nilpotent element in a semi-simple algebra, (Russian), Doklady Akad. Nauka, Volume 36, 1942, pp. 91-94
  3. ↑ Panyushev, Ernest Vinberg The work of Vladimir Morozov on Lie algebras , Transformation Groups, 15, 2010, 1001. In it you also attempt to rehabilitate the work from 1942, which in the West was long considered incomprehensible and incomplete, for example it criticized Armand Borel 1953 and Hans Freudenthal .
  4. ↑ A theorem on nilpotent elements of a semi-simple Lie algebra (Russian), Uspekhi Mat. Nauka, 15, 1960, 137-139
personal data
SURNAME Morozov, Vladimir Vladimirovich
ALTERNATIVE NAMES Морозов, Владимир Владимирович (Russian spelling)
BRIEF DESCRIPTION Russian mathematician
DATE OF BIRTH 1910
PLACE OF BIRTH Vologda
DATE OF DEATH 1975