Publications

Rota-Baxter operators

1. (with V.G. Bardakov) Rota-Baxter operators on groups, Proc. Indian Acad. Sci.: Math. Sci., 2023, 133:1, N4.

2. (with R. Kozlov) Rota-Baxter operators on Cur(sl_2), Int. Electron. J. Algebra, 2023, 33, 247-269.

3. (with T.A. Bolotina) Rota–Baxter Operators on the Simple Jordan Superalgebra  D_t, Sib. Math. J., 2022, 63:4, 637-650.

4. (with M. Goncharov) Rota-Baxter operators of nonzero weight on the matrix algebra of order three, Linear Multilinear Algebra, 2022, 70:6, 1055-1080.

5. (with V.G. Bardakov) Rota-Baxter groups, skew left braces, and the Yang-Baxter equation, J. Algebra, 2022, 596, 328-351.

6. (with A. Perepechko) Injective Rota-Baxter operators of weight zero on F[x], Mediterr. J. Math., 2021, 18:6, N267 (14 p.).

7. Rota-Baxter operators and Bernoulli polynomials, Communications in Math., 2021, 29:1, 1–14.

8. Rota-Baxter operators on unital algebras, Moscow Math. J., 2021, 21:2, 325–364.

9. Monomial Rota-Baxter operators on free commutative non-unital algebra, Sib. Electron. Math. Reports, 2020, 17, 1052–1063.

10. Rota-Baxter operators on a sum of fields, J. Algebra Its Appl., 2020, 19:6, 2050118.

11. (with D. Burde) Rota-Baxter operators and post-Lie algebra structures on semisimple Lie algebras, Communications in Algebra, 2019, 47:5, 2280–2296.

12. Universal Enveloping Lie Rota–Baxter Algebras of Pre-Lie and Post-Lie Algebras, Algebra and Logic, 2019, 58:1, 3–21.

13. Universal enveloping associative Rota-Baxter algebras of preassociative and postassociative algebra, J. Algebra, 2018, 516, 298–328.

14. (with P. Benito and A. Pozhidaev) Rota-Baxter Operators on Quadratic Algebras, Mediterr. J. Math., 2018, 15:189, N189 (23 p.).

15. Rota-Baxter operators of weight zero on simple Jordan algebra of Clifford type, Sib. Electron. Math. Reports, 2017, 14, 1524–1532.

16. Universal enveloping commutative Rota-Baxter algebras of pre- and post-commutative algebras, Axioms. Special issue ``Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2017’’, 2017, 6:4, 33.

17. (with P. Kolesnikov) Groebner-Shirshov basis of the universal enveloping Rota-Baxter algebra of a Lie algebra, J. Lie Theory, 2017, 27:3, 887–905.

18. Free Lie Rota–Baxter algebras, Siberian Math. J., 2016, 57:5, 809–818.

19. (with P. Kolesnikov) Embedding of dendriform algebras into Rota—Baxter algebras, Cent. Eur. J. Math., 2013, 11:2, 226–245.

  Preprints:

1. Spectrum of Rota-Baxter operators, arXiv:2006.02654 [math.RA], 22 p.

Loday algebras

1. Embedding of post-Lie algebras into postassociative algebras, New Trends in Algebra and Combinatorics. Proc. of the 3rd Intern. Congress in Algebra and Combinatorics (Ed. by K.P. Shum, E. Zelmanov, P. Kolesnikov, A. Wong), 2020, 57–67.

2. Embedding of pre-Lie algebras into preassociative algebras, Algebra Colloquium, 2020, 27:2, 299–310.

3. (with D. Burde) Decompositions of algebras and post-associative algebra structures, Int. J. Algebra Comput., 2020, 30:3, 451–466.

4. Poincare-Birkhoff-Witt theorem for pre-Lie and postLie algebras J. Lie Theory, 2020, 30:1, 223–238.

5. (with P. Kolesnikov) Operads of decorated trees and their duals, Comment. Math. Univ. Carolin., 2014, 55:4, 421–445.

6.  (with P. Kolesnikov) The Tits—Kantor—Koecher construction for Jordan dialgebras, Communications in Algebra, 2011, 39:2, 497–520.

  Preprints:

1. Burde's series of simple pre-Lie algebras, Sao Paulo J. Math. Sci., 2023, doi: 10.1007/s40863-023-00364-w.

Conformal algebras

1. (with R. Kozlov) Conformal Yang-Baxter equation on Cur(sl_2), J. Math. Phys., 2023, 64:1, 011704.

2. (with P. Kolesnikov; in Russian) Γ-conformal algebras of finite type for a torsion-free group Γ, Sib. Elektron. Mat. Izv., 2014, 11, 759–770.

3. Simple associative Г-conformal algebras of finite type for a torsion-free group Г, Algebra and Logic, 2013, 52:5, 371–386.

(Double) Poisson algebras

1. Universal enveloping algebra of a pair of compatible Lie brackets, Int. J. Algebra Comput., 2022, 32:7, 1335-1344.

2. (with M. Goncharov) Double Lie algebras of a nonzero weight, Adv. Math., 2022, 409 (B), 108680.

3. An example of a simple double Lie algebra, Sib. Electron. Math. Reports, 2021, 18:2, 834-844.

  Preprints:

1. (with B.K. Sartayev) Free special Gelfand-Dorfman algebra, J. Algebra Its Appl., 2023, doi: 10.1142/S0219498825500057.

Decompositions of algebras

1. Unital decompositions of M_3(C) into a sum of two subalgebras, Communications in Algebra, 2021, 49:11, 4980-5005.

Axial algebras

  Preprints: 

1. (with I. Gorshkov) Quasi-definite axial algebras of Jordan type half,Sib. Electron. Math. Rep. (accepted), 2023.

Representation theory

1. The subspace L((x1Λ...Λ xk)m) of Sm(ΛkRn), Algebra and Logic, 2010, 49:4, 305–325.

2. On the subspace L((xΛy)m) of Sm(Λ2R4), Siberian Math. J., 2009, 50:3, 395–404.

  Preprints: 

2. Symmetric power of the Grassmann variety, 2011, arXiv:1112.3577 [math.AG], 9 p.

Universal algebra

  Preprints: 

1. (with P. Kolesnikov) On the computation of Manin products for operads, 2012, arXiv:1204.0894 [math.RA], 7 p.

Algebraic graph theory

  Preprints: 

1. PC-polynomial of graph, 2018, arXiv:1808.03932 [math.CO], 118 p.

History and overview

  Preprints: 

1. (with D. Burde) In memory of Igor Dmitrievich Ado, 2019, arXiv:1908.08361 [math.HO], 3 p.