Leonid I. Vainerman

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.[3] 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.[4][5]

Leonid I. Vainerman
Леонiд Йосипович Вайнерман
Born(1946-11-15)November 15, 1946
Kyiv, Ukraine
Nationality France
Alma materTaras Shevchenko National University of Kyiv, Institute of Mathematics of National Academy of Sciences of Ukraine
Known forKac algebras, quantum groups, quantum hypergroups and quantum groupoids
Children1
Scientific career
Fieldsmathematical physics, functional analysis, algebra
InstitutionsTaras 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
ThesisBoundary value problems for second order differential equations in a Hilbert space (1974)
Doctoral advisorMyroslav L. Gorbachuk
Websitevainerman.users.lmno.cnrs.fr

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).[6][7] Vainerman was a professor at Taras Shevchenko National University of Kyiv[8][9] until 1992. He was a professor at International Solomon University from 1992 to 2002.[10][11]

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,[18] becoming a full professor in 2005. He directed three Ph.D. dissertations there (those of Pierre Fima, Camille Mével and Frank Taipe).[6][19] He has been a professor emeritus at University of Caen Normandy since 2015.[1] While at Caen, Vainerman collaborated with Dmitri Nikshych[20] and Jean-Michel Vallin.[21]

Scientific contributions

In the 1970s, Vainerman collaborated with George I. Kac (Georgii Isaakovich Kats)[22] on generalizations of Pontryagin duality to non-commutative groups and developed the concept now known as Kac algebras[23][24][25][26] (distinct from Kac-Moody algebras).

According to the French mathematician Alain Connes,[4]

The theory of Kac algebras and their duality, [was] elaborated independently by M. Enock and J. -M. Schwartz, and by G. I. Kac and L. I. Vainermann in the seventies. The subject has now reached a state of maturity

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.[5] Per Alain Connes,[4] 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 Adrian Ocneanu to the book by Enock and Schwartz,[5] Kac algebras and their actions on von Neuman algebras naturally arise in the theory of subfactors developed by Vaughan Jones.[24][27]

In his subsequent research, Vainerman obtained results on C*-algebras, Hopf algebras and quantum groups, as well as quantum hypergroups and quantum groupoids.[10][20][14][21] He is credited as a co-author or editor in more than 70 mathematics publications.[3][18]

The Timeline of quantum mechanics as well as the Timeline of atomic and subatomic physics credit Vainerman with organizing 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.[16]

References
  1. "Leonid Vainerman - personal page" (in French). The French National Centre (CNRS). Retrieved September 10, 2023.
  2. "Leonid Iosifovich Vainerman" (in Ukrainian). Kyiv Mathematical Society. Retrieved September 10, 2023.
  3. "Publication of Leonid I. Vainerman". MathSciNet. Retrieved September 10, 2023.
  4. Connes, Alain (1992). "Preface to the book 'Kac algebras'". Springer.
  5. Enock, Michel; Schwartz, Jean-Marie (1992). Kac Algebras and Duality of Locally Compact Groups. With a preface by Alain Connes. With a postface by Adrian Ocneanu. Berlin: Springer-Verlag. doi:10.1007/978-3-662-02813-1. ISBN 978-3-540-54745-7. MR 1215933.
  6. "Leonid Iosifovich Vainerman". Mathematics Genealogy Project. Retrieved September 10, 2023.
  7. Vainerman, Leonid I.; Gorbachuk, Myroslav L. (1975). "On boundary value problems for a second-order differential equation of hyperbolic type in a Hilbert space". Soviet Mathematics Doklady. 16: 401–405. Zbl 0318.35057.
  8. Vajnerman, L. I.; Kalyuzhnyj, A. A. (1994). "Quantized hypercomplex systems". Sel. Math. 13 (3): 267–281. Zbl 0842.46033.
  9. Vainerman, Leonid I.; Filimonova, Natalya B. (July 8, 1994). "Algorithms for Multispectral and Hyperspectral Imagery". SPIE Conference Proceedings. 2231: 148–155. doi:10.1117/12.179775.
  10. Chapovsky, Yu. A.; Vainerman, L. I. (1999). "Compact quantum hypergroups" (PDF). Journal of Operator Theory. 41 (2): 261–289. JSTOR 24715161. Zbl 0987.81039.
  11. "International Solomon University: Renassaince of Jewish Culture". zn.ua (in Ukrainian). October 24, 1994.
  12. Enock, Michel; Vainerman, Leonid (1996). "Deformation of a Kac algebra by an abelian subgroup". Commun. Math. Phys. 178 (3): 571–596. Zbl 0876.46042.
  13. Vainerman, L.; Kerner, R. (1996). "On special classes of n-algebras". J. Math. Phys. 37 (5): 2553–2565. Zbl 0864.17002.
  14. Vaes, Stefaan; Vainerman, Leonid (2003). "Extensions of locally compact quantum groups and the bicrossed product construction". Advances in Mathematics. 175 (1): 1–101. doi:10.1016/S0001-8708(02)00040-3. Zbl 1034.46068.
  15. "Preprints by Leonid Vainerman". Max Planck Institute for Mathematics. Retrieved September 24, 2023.
  16. Vainerman, Leonid, ed. (2003). 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. Walter de Gruyter. p. 247. ISBN 978-3-11-020005-8. Zbl 1005.00029. Retrieved September 10, 2023.
  17. Nikshych, Dmitri; Turaev, Vladimir; Vainerman, Leonid (2003). "Invariants of knots and 3-manifolds from quantum groupoids". Topology Appl. 127 (1–2): 91–123. Zbl 1021.16026.
  18. "Leonid Vainerman". ResearchGate. Retrieved September 10, 2023.
  19. "Leonid Vainerman". ABES search engine for French doctoral theses (theses.fr). Retrieved September 10, 2023.
  20. Nikshych, Dmitri; Vainerman, Leonid (2002). "Finite quantum groupoids and their applications". In Montgomery, Susan (ed.). New directions in Hopf algebras. Mathematical Sciences Research Institute Publications. Vol. 43. Cambridge University Press. pp. 211–262. ISBN 9780521815123. Zbl 1026.17017.
  21. Vainerman, Leonid; Vallin, Jean-Michel (2020). "Classifying (weak) coideal subalgebras of weak Hopf -algebras". Journal of Algebra. 550: 333–357. doi:10.1016/j.jalgebra.2019.12.026. Zbl 1446.16037.
  22. Vainerman, Leonid I.; Kats, George I. (1973). "Nonunimodular ring groups and Hopf–von Neumann algebras". Doklady Akademii Nauk SSSR. 211 (5): 1031–1034. Zbl 0296.46072.
  23. 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. (1979). "Georgii Isaakovich Kats (obituary)". Russian Mathematical Surveys. 34 (2): 213–217. doi:10.1070/RM1979v034n02ABEH002912.
  24. Izumi, Masaki; Kosaki, Hideki (2002). Kac algebras arising from composition of subfactors: General theory and classification. Memoirs of the American Mathematical Society. Vol. 750. doi:10.1090/memo/0750. Zbl 1001.46040.
  25. Vainerman, Leonid (2014). "Ideas that will outlast us". Newsletter of the European Mathematical Society. 92: 16–21. Zbl 1302.01050.
  26. Masuda, Toshihiko; Tomatsu, Reiji (2016). Classification of actions of discrete Kac algebras on injective factors. Memoirs of the American Mathematical Society. Vol. 1160. doi:10.1090/memo/1160. Zbl 1376.46052.
  27. Izumi, Masaki; Longo, Roberto; Popa, Sorin (1998). "A Galois correspondence for compact groups of automorphisms of von Neumann algebras with a generalization to Kac algebras". Journal of Functional Analysis. 155 (1): 25–63. doi:10.1006/jfan.1997.3228. Zbl 0915.46051.
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