Leonid I. Vainerman Explained

Native Name:Леонiд Йосипович Вайнерман
Native Name Lang:uk
Birth Date:15 November 1946
Birth Place:Kyiv, Ukraine
Fields:mathematical physics, functional analysis, algebra
Workplaces:Taras Shevchenko National University of Kyiv, International Solomon University, Pierre and Marie Curie University, Katholieke Universiteit Leuven, Max Planck Institute for Mathematics, University of Strasbourg, University of Caen Normandy
Thesis Title:Boundary value problems for second order differential equations in a Hilbert space
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Thesis Year:1974
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Doctoral Advisor:Myroslav L. Gorbachuk
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Known For:Kac algebras, quantum groups, quantum hypergroups and quantum groupoids
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Children:1

Leonid Iosifovich Vainerman (Ukrainian: Леонiд Йосипович Вайнерман; Russian: Леонид Иосифович Вайнерман; alternative spelling: Leonid Iosifovich Vajnerman; born November 15, 1946, in Kyiv, Ukraine) is a Ukrainian and French mathematician, professor emeritus at University of Caen Normandy.[1] [2] Vainerman's research results are in functional analysis, ordinary differential equations, operator theory, topological groups, Lie groups, and abstract harmonic analysis. In the 1970s, he co-developed Pontryagin-style dualities for non-commutative topological groups, a set of results that served as a precursor for the modern theory of quantum groups.

Education and career

Degrees and appointments in Ukraine

Vainerman studied mathematics at the Taras Shevchenko National University of Kyiv and graduated in 1969. He completed his Ph.D. (Candidate of Sciences in the USSR) in 1974 at Institute of Mathematics of National Academy of Sciences of Ukraine under the direction of Myroslav Horbachuk (Gorbachuk).[3] [4] Vainerman was a professor at Taras Shevchenko National University of Kyiv[5] [6] until 1992. He was a professor at International Solomon University from 1992 to 2002.[7]

Visiting France, Belgium and Germany

Permanent appointment in Caen

Vainerman joined the University of Caen Normandy as an associate professor in Nicolas Oresme Mathematics Laboratory, becoming a full professor in 2005. He directed three Ph.D. dissertations there (those of Pierre Fima, Camille Mével and Frank Taipe).[3] [12] He has been a professor emeritus at University of Caen Normandy since 2015.[1] While at Caen, Vainerman collaborated with Dmitri Nikshych and Jean-Michel Vallin.

Scientific contributions

In the 1970s, Vainerman collaborated with George I. Kac (Georgii Isaakovich Kats)[13] on generalizations of Pontryagin duality to non-commutative groups and developed the concept now known as Kac algebras[14] [15] [16] [17] (distinct from Kac-Moody algebras).

According to the French mathematician Alain Connes,[18] The two teams independently developed a general Pontryagin duality theory for all locally compact groups. The contributions of both teams are covered in the 1992 book by Michel Enock and Jean-Marie Schwartz on Kac algebras.[19] Per Alain Connes,[18] these results form "a general theory to characterize quantum groups among Hopf algebras, similar to the characterization of Lie groups among locally compact groups." As mentioned in the postface by to the book by Enock and Schwartz,[19] Kac algebras and their actions on von Neumann algebras naturally arise in the theory of subfactors developed by Vaughan Jones.[15] [20]

In his subsequent research, Vainerman obtained results on C*-algebras, Hopf algebras and quantum groups, as well as quantum hypergroups and quantum groupoids.[21] [22] [23] [24] He is credited as a co-author or editor in more than 70 mathematics publications.[25] [26]

Vainerman organized a meeting at the University of Strasbourg February 21–23, 2002 that assembled theoretical physicists and mathematicians specializing in quantum group and quantum groupoid applications in quantum theories beyond the Standard Model. Vainerman edited the proceedings of the meeting and had them published as a book in 2003.[27]

External links

Notes and References

  1. Web site: Leonid Vainerman - personal page . fr . The French National Centre (CNRS) . September 10, 2023.
  2. Web site: Leonid Iosifovich Vainerman . Kyiv Mathematical Society. uk. September 10, 2023.
  3. Web site: Leonid Iosifovich Vainerman . Mathematics Genealogy Project . September 10, 2023.
  4. Vainerman . Leonid I.. Gorbachuk . Myroslav L.. On boundary value problems for a second-order differential equation of hyperbolic type in a Hilbert space. 0318.35057. Soviet Mathematics Doklady. 16. 401–405. 1975 .
  5. Vajnerman, L. I. . Kalyuzhnyj, A. A. . Quantized hypercomplex systems . 0842.46033 . Sel. Math. . 13 . 3 . 267–281 . 1994.
  6. Vainerman . Leonid I.. Filimonova. Natalya B.. A. Evan. Iverson. Algorithms for Multispectral and Hyperspectral Imagery. July 8, 1994. SPIE Conference Proceedings. 2231. 148–155. 10.1117/12.179775. 123625669.
  7. Web site: International Solomon University: Renassaince of Jewish Culture . zn.ua . uk . October 24, 1994.
  8. Enock . Michel . Vainerman . Leonid . Deformation of a Kac algebra by an abelian subgroup . 0876.46042 . Commun. Math. Phys. . 178 . 3 . 571–596 . 1996. 10.1007/BF02108816 . 119863987 .
  9. Vainerman, L. . Kerner, R. . On special classes of n-algebras . 0864.17002 . J. Math. Phys. . 37 . 5 . 2553–2565 . 1996. 10.1063/1.531526 .
  10. Web site: Preprints by Leonid Vainerman . Max Planck Institute for Mathematics . September 24, 2023.
  11. Nikshych . Dmitri . Turaev . Vladimir . Vainerman . Leonid . Invariants of knots and 3-manifolds from quantum groupoids . 1021.16026 . Topology Appl. . 127 . 1–2 . 91–123 . 2003. 10.1016/S0166-8641(02)00055-X . 16661718 . free . math/0006078 .
  12. Web site: Leonid Vainerman . ABES search engine for French doctoral theses (theses.fr) . September 10, 2023.
  13. Vainerman . Leonid I.. Kats. George I.. Nonunimodular ring groups and Hopf–von Neumann algebras. Doklady Akademii Nauk SSSR. 211. 5. 1973. 1031–1034. 0296.46072.
  14. Berezanskii . Yu. M. . Berezin . F. A.. Bogolyubov . N. N.. Vainerman . L. I.. Daletskii . Yu. L.. Kirillov . A. A.. Palyutkin . V. G.. Khatset . B. I.. Èidel'man . S. D.. Georgii Isaakovich Kats (obituary). Russian Mathematical Surveys. 34. 2. 1979. 213–217. 10.1070/RM1979v034n02ABEH002912. 250754802 .
  15. Book: Izumi . Masaki. Kosaki . Hideki . Kac algebras arising from composition of subfactors: General theory and classification. 1001.46040. Memoirs of the American Mathematical Society. 158. 2002. 750. 10.1090/memo/0750.
  16. Vainerman . Leonid. Ideas that will outlast us. 1302.01050 . Newsletter of the European Mathematical Society. 92. 16–21 . 2014.
  17. Book: Masuda . Toshihiko. Tomatsu . Reiji . Classification of actions of discrete Kac algebras on injective factors. 1376.46052. Memoirs of the American Mathematical Society. 245. 2016. 1160. 10.1090/memo/1160. 119321613.
  18. Book: Connes, Alain . Preface to the book 'Kac algebras' . 1992 . Springer. 10.1007/978-3-662-02813-1 . 978-3-642-08128-6 .
  19. Book: Enock. Michel. Schwartz. Jean-Marie. Kac Algebras and Duality of Locally Compact Groups. 1992. Springer-Verlag. 978-3-540-54745-7. With a preface by Alain Connes. With a postface by Adrian Ocneanu. Berlin. 1215933. 10.1007/978-3-662-02813-1.
  20. Izumi . Masaki. Longo . Roberto. Popa . Sorin . Sorin Popa. A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras. 0915.46051. Journal of Functional Analysis. 155. 1. 25–63 . 1998. 10.1006/jfan.1997.3228 . free. funct-an/9604004.
  21. Chapovsky . Yu. A.. Vainerman . L. I.. Compact quantum hypergroups. 0987.81039. Journal of Operator Theory. 41. 2. 261–289. 1999. 24715161.
  22. Book: Nikshych . Dmitri. Vainerman . Leonid. Finite quantum groupoids and their applications. 1026.17017. 9780521815123 . Montgomery . Susan . New directions in Hopf algebras. Cambridge University Press. Mathematical Sciences Research Institute Publications. 43. 211–262. 2002.
  23. Vaes . Stefaan. Vainerman . Leonid . Extensions of locally compact quantum groups and the bicrossed product construction. 1034.46068. Advances in Mathematics. 175. 1. 1–101. 2003. 10.1016/S0001-8708(02)00040-3 . free. math/0101133.
  24. Vainerman . Leonid. Vallin . Jean-Michel . Classifying (weak) coideal subalgebras of weak Hopf

    C*

    -algebras. 1446.16037. Journal of Algebra. 550. 333–357. 2020. 10.1016/j.jalgebra.2019.12.026. free. 1904.07602.
  25. Web site: Publication of Leonid I. Vainerman . . September 10, 2023.
  26. Web site: Leonid Vainerman . September 10, 2023.
  27. Book: Leonid. Vainerman. Locally Compact Quantum Groups and Groupoids: Proceedings of the Meeting of Theoretical Physicists and Mathematicians, Strasbourg, February 21–23, 2002. IRMA Lectures in Mathematics and Theoretical Physics. 2 . September 10, 2023. 2003. Walter de Gruyter. 978-3-11-020005-8. 247. 1005.00029.

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