Publications
2025
[1]
V. Abramov. Biunits of ternary algebra of hypermatrices. In: V. Dvoeglazov (Ed.), Mathematical Problems in Relativity, Gravitation, Cosmology, Nova Science Publishers, 1–20 (2025).
[2]
V. Abramov, N. Sovetnikov. Odd and even derivations, transposed Poisson superalgebra and 3-Lie superalgebra. Proceedings of the Estonian Academy of Sciences 74 (4), 487–499 (2025). DOI
[3]
A. M. Aader, V. Abramov, O. Liivapuu. Associative ternary algebras and ternary Lie algebras at cube roots of unity. Mathematics 13 (24), 3894 (2025). DOI
2024
[1]
V. Abramov. Ternary Associativity and Ternary Lie Algebras at Cube Roots of Unity. Axioms 13 (10), 687 (2024). DOI
[2]
V. Abramov, O. Liivapuu. Transposed Poisson superalgebra. Proceedings of the Estonian Academy of Sciences 73 (1), 50–59 (2024). DOI
[3]
V. Abramov, O. Liivapuu. SO(3)-Irreducible Geometry in Complex Dimension Five and Ternary Generalization of Pauli Exclusion Principle. Universe 10 (1), 1 (2024). DOI
2023
[1]
V. Abramov, S. Groote, P. Lätt. Algebra with ternary cyclic relations, representations and quark model. Proceedings of the Estonian Academy of Sciences 72 (1), 61–76 (2023). DOI
[2]
V. Abramov, E. Zappala. 3-Lie Algebras, Ternary Nambu-Lie Algebras and the Yang-Baxter Equation. Journal of Geometry and Physics 183, 104867 (2023). DOI
[3]
V. Abramov. Ternary algebras associated with irreducible tensor representations of SO(3) and the quark model. International Journal of Geometric Methods in Modern Physics 20 (5), 2350076 (2023). DOI
2022
[1]
V. Abramov, P. Lätt. Karen Uhlenbeck, geomeetria ja matemaatiline füüsika. Eesti Matemaatika Seltsi Aastaraamat 2019, 8–34 (2022).
2020
[1]
V. Abramov. Weil Algebra, 3-Lie Algebra and B.R.S. Algebra. In: S. Silvestrov, A. Malyarenko, M. Rancic (Eds.), Algebraic Structures and Applications, SPAS 2017, Springer Proceedings in Mathematics and Statistics, 317, Springer International Publisher, 1–12 (2020). DOI
[2]
V. Abramov, R. Kerner, O. Liivapuu. Algebras with ternary composition law combining Z2 and Z3 gradings. In: S. Silvestrov, A. Malyarenko, M. Rancic (Eds.), Springer Proceedings in Mathematics and Statistics, Springer, 13–45 (2020). DOI
[3]
V. Abramov, P. Lätt. Ternary Lie Superalgebras and Nambu-Hamilton Equation in Superspace. In: Springer Proceedings in Mathematics & Statistics, 317, 47–80 (2020). DOI
[4]
V. Abramov, P. Lätt. Induced 3-Lie algebras, superalgebras and induced representations. Proceedings of the Estonian Academy of Sciences 69 (2), 116–133 (2020). DOI
[5]
V. Abramov, S. Silvestrov. 3-Hom-Lie Algebras Based on σ-Derivation and Involution. Advances in Applied Clifford Algebras 30 (3), 45 (2020). DOI
2019
[1]
V. Abramov. 3-Lie Superalgebras Induced by Lie Superalgebras. Axioms 8 (1), 21 (2019). DOI
[2]
V. Abramov, O. Liivapuu. Connections in Euclidean and non-commutative geometry. In: S. Bernstein (Ed.), Topics in Clifford Analysis - A Special Volume in Honor of Wolfgang Sprössig, Trends in Mathematics, Springer, 279–311 (2019). DOI
2018
[1]
V. Abramov. Quantum Super Nambu Bracket of Cubic Supermatrices and 3-Lie Superalgebra. Advances in Applied Clifford Algebras 28 (2), 33 (2018). DOI
[2]
V. Abramov. Nambu-Poisson bracket on superspace. International Journal of Geometric Methods in Modern Physics 15 (11), 1850190 (2018). DOI
[3]
V. Abramov. Generalization of Nambu-Hamilton equation and extension of Nambu-Poisson bracket to superspace. Universe 4 (10), 106 (2018). DOI
[4]
V. Abramov, O. Liivapuu, A. Makhlouf. (q,σ,τ)-Differential Graded Algebras. Universe 4 (12), 138 (2018). DOI
2017
2016
[1]
V. Abramov. Noncommutative Galois Extension and Graded q-Differential Algebra. Advances in Applied Clifford Algebras 26 (1), 1–11 (2016).
2015
[1]
V. Abramov, O. Liivapuu. N-complex, graded q-differential algebra and N-connection on modules. Journal of Generalized Lie Theory and Applications 9 (2), 1–11 (2015). DOI
[2]
V. Abramov, O. Liivapuu. Graded q-Differential Algebra Approach to Chern-Simons Form. Applied Mathematics & Information Sciences 9 (1), 29–38 (2015). DOI
2014
[1]
V. Abramov, O. Liivapuu. Graded q-Differential Polynomial Algebra of Connection Form. In: A. Makhlouf, E. Paal et al. (Eds.), Algebra, Geometry and Mathematical Physics, Springer Proceedings in Mathematics and Statistics, 85, Springer, 361–378 (2014). DOI
[2]
V. Abramov, J. Vajakas. Geometric Approach to Ghost Fields. In: A. Makhlouf, E. Paal, S. D. Silvestrov, A. Stolin (Eds.), Algebra, Geometry and Mathematical Physics. AGMP, Mulhouse, France, October 2011, Springer Proceedings in Mathematics & Statistics, 85, Springer, 475–488 (2014). DOI
2009
[1]
V. Abramov, R. Kerner, O. Liivapuu, S. Shitov. Algebras with ternary law of composition and their realization by cubic matrices. J. Gen. Lie Theory Appl. 3, 77–94 (2009).
2008
[1]
V. Abramov, E. Paal, V. Silvestrov, A. Stolin. Proceedings of the 3rd Baltic-Nordic Workshop "Algebra, Geometry, and Mathematical Physics" in Göteborg, Sweden, October 11-13, 2007, dedicated to memory of Professor Isaiah Kantor (1936-2006). Journal of Generalized Lie Theory and Applications 2 (3), 109 (2008).
2007
[1]
V. Abramov. Algebra Forms with dᴺ=0 on Quantum Plane. Generalized Clifford Algebra Approach. Advances in Applied Clifford Algebras 17, 577–588 (2007).
2006
[1]
V. Abramov. On a graded q-differential algebra. African Journal of Mathematical Physics 3 (1), 181–184 (2006).
[2]
V. Abramov. Generalization of superconnection in non-commutative geometry. Proceedings of the Estonian Academy of Sciences. Physics. Mathematics 55 (1), 3–15 (2006).
[3]
V. Abramov, O. Liivapuu. Geometric approach to BRST-symmetry and ℤₙ-generalization of superconnection. Journal of Nonlinear Mathematical Physics 13, 9–20 (2006).
[4]
V. Abramov. On a graded q-differential algebra. Journal of Nonlinear Mathematical Physics 13, 1–8 (2006).
2004
[1]
V. Abramov. On the development of differential geometry in Estonia. In: M. Abel (Ed.), Recent developments in mathematics: FinEst Math 2002, Finnish-Estonian colloquium; Tallinn, Estonia; 27.-29.05.2002, Mathematics studies, 2, Estonian Mathematical Society, 20–41 (2004).
2002
[1]
V. Abramov, Ü. Lumiste. Faddeev-Popov ghost. In: M. Hazewinkel (Ed.), Encyclopaedia of Mathematics, Supplement III, Encyclopaedia of Mathematics, Kluwer, 147–148 (2002).
[2]
V. Abramov, N. Bazunova. Algebra of differential forms with exterior differential d³=0 in dimension one. In: E. Kapuscik, A. Horzela (Eds.), Quantum theory and symmetries: 2nd international symposium; Kraków, Poland; 18.-21.07.2001, World Scientific Publishing Co, 198–205 (2002).
2000
[1]
V. Abramov, N. Bazunova. Exterior calculus with d³=0 on a free associative algebra and reduced with d³=0 on a free associative algebra and reduced. In: New symmetries and integrable models: Proceedings of XIV Max Born symposium, Karpacz, Poland, September 21-24, 1999, 3–7 (2000).
[2]
V. Abramov, R. Kerner. Exterior differentials of higher order and their covariant generalization. Journal of Mathematical Physics 41 (8), 5598–5614 (2000).
1999
[1]
V. Abramov, M. Rahula. Differential geometry of 20th century and geometric research in Tartu. In: V. Abramov, M. Rahula, K. Riives (Eds.), Ülo Lumiste mathematician, Estonian Mathematical Society, 103–123 (1999).
[2]
R. Kerner, V. Abramov. On certain realizations of the q-deformed exterior differential calculus. Reports on Mathematical Physics 43, 179–194 (1999).
1998
[1]
V. Abramov. On realizations of exterior calculus with dᴺ=0. Czechoslovak Journal of Physics 48 (11), 1265–1272 (1998).
1997
[1]
V. Abramov, R. Kerner, B. LeRoy. Hypersymmetry: A ℤ₃-graded generalization of supersymmetry. Journal of Mathematical Physics 38 (3), 1650–1669 (1997).