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 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.

Publications

  1. F. Díaz García, A. Krutov, R. Ó Buachalla, P. Somberg, K. R. Strung, Positive line bundles over the irreducible quantum flag manifolds, Lett. Math. Phys. (2022) 30 p. (to appear), arXiv:1912.08802 [math.QA] OWP-2020-01
  2. 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.
  3. 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
  4. 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
  5. 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)
  6. 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].
  7. 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]
  8. 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
  9. 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)
  10. 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)
  11. 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)
  12. 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
  13. 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

Back to menu

Preprints

  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. A. Krutov, D. Leites, J. Shang, Duflo-Serganova homology for exceptional modular Lie superalgebras with Cartan matrix, 20 p. arXiv:2008.12033 [math.RT]

Back to menu

Talks at conferences, workshops and research seminars

Back to menu

Other Academic Activity

Research visits

Visitors

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

Back to menu