Zhelyabin, Viktor Nikolaevich

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Total publications: 34
Scientific articles: 32

Number of views:
This page:5615
Abstract pages:10331
Full texts:2148
Doctor of physico-mathematical sciences (1998)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail: ,
Keywords: ring theory, Jordan algebras, Banah algebras, Lie algebras, coalgebras.


A class of Jordan bialgebras related to the "Jordan analog" of the classical Yang–Baxter equation was introduced. It had proved this every Jordan bialgebra defined on a finite-dimensional semisimple Jordan algebra belongs to that class. The triangle and the quasitriangle Jordan bialgebras were defined in agreement with corresponding concepts for the Lie bialgebras, and a characterization the finite-dimensional Jordan algebras admitting a nontrivial structure of a quasitriangle bialgebra was obtained.


Graduated from Faculty of Mathematics and Mechanics of Novosibirsk State University (NSU) in 1965 (department of algebra and mathematical logik). Ph.D. thesis was defended in 1981. D.Sci. thesis was defended in 1998. A list of my works contains more than 30 titles. Leder the research seminar at NSU on algebra.

Main publications:
  • On a class of Jordan D-bialgebras // St. Petersburg Math. J., 2000, 11, 4, 589–609.
  • Jordan D-bialgebras and sympectic forms on Jordan algebras // Siberian Advances in Mathematics, 2000, 10, 2, 134–142.
  • Jordan bialgebras and their relation to Lie bialgebras // Algebra and Logic, 1997, 36, 1, 3–25.
  • Finite-Dimensional Jordan Algebras Admitting the Structure of a Jordan Bialgebra // Algebra and Logic, 1999, 38, 1, 40–67.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. V. N. Zhelyabin, “Addition to Block's theorem and to Popov's theorem on differentially simple algebras”, Sib. Èlektron. Mat. Izv., 16 (2019),  1375–1384  mathnet
2. V. N. Zhelyabin, A. S. Panasenko, “Nearly finite-dimensional Jordan algebras”, Algebra Logika, 57:5 (2018),  522–546  mathnet; Algebra and Logic, 57:5 (2018), 336–352  isi  scopus
3. V. N. Zhelyabin, “Structure of some unital simple Jordan superalgebras with associative even part”, Sibirsk. Mat. Zh., 59:6 (2018),  1322–1337  mathnet  elib; Siberian Math. J., 59:6 (2018), 1051–1062  isi  scopus
4. V. N. Zhelyabin, A. S. Panasenko, “Nil Ideals of Finite Codimension in Alternative Noetherian Algebras”, Mat. Zametki, 101:3 (2017),  395–402  mathnet  mathscinet  elib; Math. Notes, 101:3 (2017), 460–466  isi  scopus
5. V. N. Zhelyabin, A. I. Shestakov, “Alternative and Jordan algebras admitting ternary derivations with invertible values”, Sib. Èlektron. Mat. Izv., 14 (2017),  1505–1523  mathnet  isi
6. V. N. Zhelyabin, A. S. Panasenko, “Herstein's construction for just infinite superalgebras”, Sib. Èlektron. Mat. Izv., 14 (2017),  1317–1323  mathnet
7. V. N. Zhelyabin, A. S. Zakharov, “Some constructions for Jordan superalgebras with associative even part”, Algebra i Analiz, 28:2 (2016),  97–113  mathnet  mathscinet  elib; St. Petersburg Math. J., 28:2 (2017), 197–208  isi  scopus
8. V. N. Zhelyabin, “Simple Jordan superalgebras with associative nil-semisimple even part”, Sibirsk. Mat. Zh., 57:6 (2016),  1262–1279  mathnet  elib; Siberian Math. J., 57:6 (2016), 987–1001  isi  scopus
9. V. N. Zhelyabin, A. S. Zakharov, “Speciality of Jordan Superalgebras Related to Novikov–Poisson Algebras”, Mat. Zametki, 97:3 (2015),  359–367  mathnet  mathscinet  zmath  elib; Math. Notes, 97:3 (2015), 341–348  isi  scopus
10. V. N. Zhelyabin, “$(-1,1)$-superalgebras of vector type: Jordan superalgebras of vector type and their universal envelopings”, Sibirsk. Mat. Zh., 56:3 (2015),  520–536  mathnet  mathscinet  elib; Siberian Math. J., 56:3 (2015), 411–424  isi  elib  scopus
11. V. N. Zhelyabin, M. E. Goncharov, “An example of differentially simple Lie algebra which is not a free module over its centroid”, Sib. Èlektron. Mat. Izv., 11 (2014),  915–920  mathnet
12. V. N. Zhelyabin, A. A. Popov, I. P. Shestakov, “The coordinate ring of an $n$-dimensional sphere and some examples of differentially simple algebras”, Algebra Logika, 52:4 (2013),  416–434  mathnet  mathscinet; Algebra and Logic, 52:4 (2013), 277–289  isi  scopus
13. M. E. Goncharov, V. N. Zhelyabin, “Embedding Mal'tsev coalgebras into Lie coalgebras with triality”, Algebra Logika, 52:1 (2013),  34–56  mathnet  mathscinet  zmath; Algebra and Logic, 52:1 (2013), 24–40  isi  scopus
14. V. N. Zhelyabin, “Examples of prime Jordan superalgebras of vector type and superalgebras of Cheng–Kac type”, Sibirsk. Mat. Zh., 54:1 (2013),  49–56  mathnet  mathscinet; Siberian Math. J., 54:1 (2013), 33–39  isi  scopus
15. V. N. Zhelyabin, “New examples of simple Jordan superalgebras over an arbitrary field of characteristic zero”, Algebra i Analiz, 24:4 (2012),  84–96  mathnet  mathscinet  zmath  elib; St. Petersburg Math. J., 24:4 (2013), 591–600  isi  elib  scopus
16. M. E. Goncharov, V. N. Zhelyabin, “Mikheev's construction for Mal'tsev coalgebras”, Algebra Logika, 51:5 (2012),  668–671  mathnet  mathscinet  zmath; Algebra and Logic, 51:5 (2012), 445–447  isi  scopus
17. V. N. Zhelyabin, “Jordan superalgebras of vector type and projective modules”, Sibirsk. Mat. Zh., 53:3 (2012),  566–579  mathnet  mathscinet; Siberian Math. J., 53:3 (2012), 450–460  isi  scopus
18. V. N. Zhelyabin, I. B. Kaygorodov, “On $\delta$-superderivations of simple superalgebras of Jordan brackets”, Algebra i Analiz, 23:4 (2011),  40–58  mathnet  mathscinet  zmath  elib; St. Petersburg Math. J., 23:4 (2012), 665–677  isi  elib  scopus
19. V. N. Zhelyabin, “Differential algebras and simple Jordan superalgebras”, Mat. Tr., 12:2 (2009),  41–51  mathnet  mathscinet; Siberian Adv. Math., 20:3 (2010), 223–230
20. V. N. Zhelyabin, “Universal envelopes of Malcev Algebras: Pointed Moufang bialgebras”, Sibirsk. Mat. Zh., 50:6 (2009),  1285–1304  mathnet  mathscinet  elib; Siberian Math. J., 50:6 (2009), 1011–1026  isi  elib  scopus
21. V. N. Zhelyabin, A. S. Tikhov, “Novikov–Poisson algebras and associative commutative derivation algebras”, Algebra Logika, 47:2 (2008),  186–202  mathnet  mathscinet  zmath; Algebra and Logic, 47:2 (2008), 107–117  isi  scopus
22. V. N. Zhelyabin, I. P. Shestakov, “The Chevalley and Costant theorems for Mal'tsev algebras”, Algebra Logika, 46:5 (2007),  560–584  mathnet  mathscinet  zmath  elib; Algebra and Logic, 46:5 (2007), 303–317  isi  elib  scopus
23. V. N. Zhelyabin, “The coradical of a Jordan (alternative) coalgebra and the quasiregular radical of its dual algebra”, Mat. Zametki, 80:4 (2006),  509–515  mathnet  mathscinet  zmath  elib; Math. Notes, 80:4 (2006), 485–490  isi  scopus
24. V. N. Zhelyabin, “Dual coalgebras of Jordan bialgebras and superalgebras”, Sibirsk. Mat. Zh., 46:6 (2005),  1302–1315  mathnet  mathscinet  zmath; Siberian Math. J., 46:6 (2005), 1050–1061  isi
25. V. N. Zhelyabin, I. P. Shestakov, “Simple special Jordan superalgebras with associative even part”, Sibirsk. Mat. Zh., 45:5 (2004),  1046–1072  mathnet  mathscinet  zmath  elib; Siberian Math. J., 45:5 (2004), 860–882  isi
26. V. N. Zhelyabin, “Jordan (super)coalgebras and Lie (super)coalgebras”, Sibirsk. Mat. Zh., 44:1 (2003),  87–111  mathnet  mathscinet  zmath; Siberian Math. J., 44:1 (2003), 73–92  isi
27. V. N. Zhelyabin, “Simple Special Jordan Superalgebras with Associative Nil-Semisimple Even Part”, Algebra Logika, 41:3 (2002),  276–310  mathnet  mathscinet  zmath  elib; Algebra and Logic, 41:3 (2002), 152–172  scopus
28. V. N. Zhelyabin, “Jordan D-Bialgebras and Symplectic Forms on Jordan Algebras”, Mat. Tr., 3:1 (2000),  38–47  mathnet  mathscinet  zmath; Siberian Adv. Math., 10:2 (2000), 142–150
29. V. N. Zhelyabin, “On a class of Jordan $D$-bialgebras”, Algebra i Analiz, 11:4 (1999),  64–94  mathnet  mathscinet  zmath; St. Petersburg Math. J., 11:4 (2000), 589–609
30. V. N. Zhelyabin, “Jordan bialgebras of symmetric elements and Lie bialgebras”, Sibirsk. Mat. Zh., 39:2 (1998),  299–316  mathnet  mathscinet  zmath; Siberian Math. J., 39:2 (1998), 261–276  isi
31. Sh. A. Ayupov, A. A. Adizov, V. N. Zhelyabin, “Multiplicative maps of ordered Jordan algebras”, Mat. Zametki, 51:2 (1992),  3–8  mathnet  mathscinet  zmath; Math. Notes, 51:2 (1992), 105–109  isi
32. Sh. A. Ayupov, V. N. Zhelyabin, “Compatibility of elements in Jordan algebras”, Mat. Zametki, 37:3 (1985),  305–312  mathnet  mathscinet  zmath; Math. Notes, 37:3 (1985), 173–176  isi

33. Yu. L. Ershov, S. S. Goncharov, V. D. Mazurov, B. S. Baizhanov, B. Sh. Kulpeshov, P. E. Alaev, A. V. Vasil'ev, E. V. Vasil'ev, E. P. Vdovin, V. V. Verbovskii, A. A. Vikent'ev, D. Yu. Vlasov, M. A. Grechkoseeva, V. N. Zhelyabin, P. S. Kolesnikov, V. M. Kopytov, L. L. Maksimova, I. A. Mal'tsev, A. S. Morozov, A. A. Nikitin, E. V. Ovchinnikova, S. P. Odintsov, D. E. Pal'chunov, N. A. Peryazev, A. G. Pinus, L. N. Pobedin, A. P. Pozhidaev, B. Poizat, V. G. Puzarenko, D. O. Revin, V. N. Remeslennikov, N. S. Romanovskii, A. N. Ryaskin, S. S. Starchenko, A. A. Stepanova, S. V. Sudoplatov, E. I. Timoshenko, D. A. Tusupov, N. G. Khisamiev, V. A. Churkin, Z. Chatzidakis, M. V. Schwidefsky, K. M. Shegirov, I. P. Shestakov, “Evgenii Andreevich Palyutin (1945–2018)”, Sib. Èlektron. Mat. Izv., 16 (2019),  1–10  mathnet
34. L. A. Bokut', E. S. Golod, R. I. Grigorchuk, V. N. Zhelyabin, V. G. Kats, A. R. Kemer, V. V. Kirichenko, P. S. Kolesnikov, S. S. Kutateladze, V. N. Latyshev, Yu. N. Maltsev, G. A. Margulis, A. V. Mikhalev, A. G. Myasnikov, S. P. Novikov, A. Yu. Ol'shanskii, A. N. Parshin, V. P. Platonov, Yu. G. Reshetnyak, N. S. Romanovskii, I. A. Taimanov, O. G. Kharlampovich, V. K. Kharchenko, L. N. Shevrin, I. P. Shestakov, A. V. Yakovlev, “Efim Isaakovich Zelmanov is 60 years old”, Uspekhi Mat. Nauk, 71:4(430) (2016),  193–199  mathnet  mathscinet  elib; Russian Math. Surveys, 71:4 (2016), 793–800  isi

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