dr. Andrey Krutov

Address: Institute of Mathematics CAS
Žitná 25
115 67 Praha 1
Czech Republic

Emails: a.o.krutov at gmail dot com GPG key, krutov at math dot cas dot cz GPG key.

MR author ID: 912066, Google Scholar ID: UIOivHUAAAAJ, arXiv ID: krutov_a_1
Andrey Krutov

I am a postdoctoral researcher at Institute of Mathematics of Czech Academy of Sciences (Prague, Czechia). My research interests includes representation theory of Lie (super)algebra, geometry of integrable systems, quantum groups and noncommutative geometry. I got my PhD in June 2014 at University of Groningen, under supervision of Dr. Arthemy Kiselev and Prof. Dr. Jaap Top.


  1. A. Krutov, A. Lebedev, D. Leites, I.Shchepochkina, Nondegenerate invariant symmetric bilinear forms on simple Lie superalgebras in characteristic 2, Linear Algebra Appl. 649 (2022), 1–21, arXiv:2102.11653 Updated version of OWP-2020-02.
  2. F. Díaz García, A. Krutov, R. Ó Buachalla, P. Somberg, K. R. Strung, Holomorphic relative Hopf modules over the irreducible quantum flag manifolds, Lett. Math. Phys. 111 (2021), no. 1, 24, arXiv:2005.09652 [math.QA] link
  3. A. V. Kiselev, A. O. Krutov, On the (non)removability of spectral parameters in \(\mathbb{Z}_2\)-graded zero-curvature representations and its applications, Acta Appl. Math. 160 (2019), no. 1, 129–167, arXiv:1301.7143 [math.DG] link
  4. A. Krutov, A. Lebedev, On gradings modulo 2 of simple lie algebras in characteristic 2, SIGMA Symmetry Integrability Geom. Methods Appl. 14 (2018), no. 130, 27, arXiv:1711.00638 [math.RT] link (Open access)
  5. S. Bouarroudj, A. Krutov, D. Leites, I. Shchepochkina, Non-degenerate invariant (super)symmetric bilinear forms on simple Lie (super)algebras, Algebr. Represent. Theory 21 (2018), no.5, 897–941, arXiv:1806.05505 [math.RT].
  6. A. V. Kiselev, A. O. Krutov, T.Wolf, Computing symmetries and recursion operators of evolutionary super-systems using the SsTools environment, Nonlinear Systems and Their Remarkable Mathematical Structures (N. Euler, ed.), vol. 1, CRC Press, Boca Raton, FL, 2018, pp. 390–407, arXiv:1805.12397 [nlin.SI]
  7. S. Bouarroudj, A. Krutov, A. Lebedev, D. Leites, I. Shchepochkina, On restricted Lie (super)algebras in characteristic 3, Funct. Anal. Appl. 52 (2018), no. 1, 49–52, arXiv:1809.08582 [math.RT] link
  8. A. V. Kiselev, A. O. Krutov, Gardner's deformation of the Krasil'shchik–Kersten system, J. Phys.: Conf. Ser. 621 (2015), no. 1, 19, Group Analysis of Differential Equations and Integrable Systems (GADEISVII) (June 15–19, 2014; Larnaca, Cyprus). arXiv:1409.6688 [nlin.SI], link (Open access)
  9. A. V. Kiselev, A. O. Krutov, Non-Abelian Lie algebroids over jet spaces, J. Nonlin. Math. Phys. 21 (2014), no. 2, 188–213, arXiv:1305.4598 [math.DG] link (Open access)
  10. A. V. Kiselev, A. O. Krutov, Gardner's deformations as generators of new integrable systems, J. Phys.: Conf. Ser. 482 (2014), no. 1, 6, Physics and Mathematics of Nonlinear Phenomena 2013, (June 22–29, 2013; Gallipoli, Italy). arXiv:1312.6941 [nlin.SI] link (Open access)
  11. A. V. Kiselev, A. O. Krutov, Gardner's deformations of the graded Korteweg–de Vries equations revisited, J. Math. Phys. 53 (2012), no. 10, 103511, 18, arXiv:1108.2211 [nlin.SI] link
  12. V. Hussin, A. V. Kiselev, A. O. Krutov, T. Wolf, N=2 supersymmetric a=4-Korteweg–de Vries hierarchy derived via Gardner's deformation of Kaup–Boussinesq equation, J. Math. Phys. 51 (2010), no. 8, 083507, 19, arXiv:0911.2681 [nlin.SI] link

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  1. A. Krutov, P. Pandžić, Cubic Dirac operator for \(U_q(\mathfrak{sl}_2)\), 14 p. arXiv:2209.09591, [math.RT]
  2. A. O. Krutov, R. Ó Buachalla, K. R. Strung, Nichols algebras and quantum principal bundles, 31 p. arXiv:1701.04394 [math.QA]
  3. F. Díaz García, A. Krutov, R. Ó Buachalla, P. Somberg, K. R. Strung, Positive line bundles over the irreducible quantum flag manifolds, 30 p. arXiv:1912.08802 [math.QA] OWP-2020-01
  4. A. Krutov, D. Leites, J. Shang, Duflo-Serganova homology for exceptional modular Lie superalgebras with Cartan matrix, 20 p. arXiv:2008.12033 [math.RT]

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Talks at conferences, workshops and research seminars

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Other Academic Activity

Research visits


Graduate Schools

I attended five graduate schools in geometry of partial differential equations (Kostroma, 2008, 2009; Gdynia 2012; Kouty nad Desnou, 2013; Pereslavl-Zalessky, 2015), the graduate school and the conference in Geometry & Quantum Theory of the GQT-cluster (Zeist, 2014), Advanced School on Integrability (Warsaw, 2017), Mini School on Schubert Calculus (Guangzhou, 2017).

Other Service

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