dr. Andrey Krutov

Address: Mathematical Institute of Charles University
Sokolovská 49/83, 186 75 Praha 8
Czech Republic

Emails: a.o.krutov at gmail dot com GPG key, andrey dot krutov at matfyz dot cuni dot cz

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

I am a researcher at the Mathematical Institute of Charles University (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.

Conference on quantum groups in Zagreb

Toother with K. Grizelj, P. Pandžić, and A. Prlić, I'm organizing a conference on quantum groups (CaLISTA WG3 meeting) in Zagreb (25.09 - 26.09). The details can be found on the website of the conference (the website is under construction at the moment and will be available soon).

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Publications

  1. A. O. Krutov, R. Ó Buachalla, K. R. Strung, Nichols algebras and quantum principal bundles, Int. Math. Res. Not. IMRN (2023), no. 23, 20076–20117. arXiv:1701.04394 [math.QA]
  2. F. Díaz García, A. Krutov, R. Ó Buachalla, P. Somberg, K. R. Strung, Positive line modules over the irreducible quantum flag manifolds, Lett. Math. Phys. 112 (2022), no. 6, 33 p., arXiv:1912.08802 [math.QA] OWP-2020-01
  3. 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.
  4. 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 p., arXiv:2005.09652 [math.QA] link
  5. 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
  6. 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 p., arXiv:1711.00638 [math.RT] link (Open access)
  7. 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].
  8. 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]
  9. 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
  10. A. V. Kiselev, A. O. Krutov, Gardner's deformation of the Krasil'shchik–Kersten system, J. Phys.: Conf. Ser. 621 (2015), no. 1, 19 p., Group Analysis of Differential Equations and Integrable Systems (GADEISVII) (June 15–19, 2014; Larnaca, Cyprus). arXiv:1409.6688 [nlin.SI], link (Open access)
  11. 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)
  12. A. V. Kiselev, A. O. Krutov, Gardner's deformations as generators of new integrable systems, J. Phys.: Conf. Ser. 482 (2014), no. 1, 6 p., Physics and Mathematics of Nonlinear Phenomena 2013, (June 22–29, 2013; Gallipoli, Italy). arXiv:1312.6941 [nlin.SI] link (Open access)
  13. 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 p., arXiv:1108.2211 [nlin.SI] link
  14. 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 p., arXiv:0911.2681 [nlin.SI] link

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Preprints

  1. A. Krutov, P. Pandžić, Quantised \(\mathfrak{sl}_2\)-differential algebras, 10 p. arXiv:2403.08521 [math.QA]
  2. A. Krutov, D. Leites, I. Shchepochkina, Non-integrable distributions with simple infinite-dimensional Lie superalgebra of symmetries, 51 p. arXiv:2309.16370 [math.DG]
  3. A. O. Krutov, R. Ó Buachalla, Curvature of positive relative line module over the quantum projective spaces, 18 p. arXiv:2309.16612 [math.QA]
  4. A. Krutov, P. Pandžić, Cubic Dirac operator for \(U_q(\mathfrak{sl}_2)\), 14 p. arXiv:2209.09591 [math.RT]
  5. 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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SuperLie

I'm a current maintener of the SuperLie package for Mathematica. SuperLie was originally developed by Pavle Grozman. The details can be found at the github page of the package. The new release is expecting soon!

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Talks at conferences, workshops, and research seminars

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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

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