Invariants of classical linear groups,
generating system,
system of parameters,
relations between generators,
semi-invariants of quivers,
nilalgebra, matrix algebra
nilpotency degree.
Ivan Kaygorodov, Artem Lopatin and Yury Popov, “Jordan algebras admitting derivations with invertible values”, Communications in Algebra, 46:1 (2018), 69–81
Artem Lopatin, “Minimal system of generators for O(4)-invariants of two skew-symmetric matrices”, Linear and Multilinear Algebra, 66:2 (2018), 347–356 http://www.tandfonline.com/doi/full/10.1080/03081087.2017.1298563
Ivan Kaygorodov, Artem Lopatin, Yury Popov, “The structure of simple noncommutative Jordan superalgebras”, Mediterranean Journal of Mathematics, 15:2 (2018), Art. 33 , 20 pp. https://link.springer.com/article/10.1007/s00009-018-1084-1
Ivan Kaygorodov, Artem Lopatin, Yury Popov, “Separating invariants for 2x2 matrices”, Linear Algebra and its Applications, 559 (2018), 114–124 https://www.sciencedirect.com/science/article/pii/S0024379518303835
Artem Lopatin, Aleksandr Tsarev, Tongsou Wu, “On the lattices of multiply composition formations of finite groups”, Bulletin of the international mathematical virtual institute, 6:2 (2016), 219-226 http://www.imvibl.org/buletin/bulletin_imvi_6_2_2016/bulletin_imvi_6_2_2015_219_226.pdf
2015
6.
A. A. Lopatin, “Orthogonal matrix invariants”, J. Generalized Lie Theory Appl, 9:S1 (2015), 007 , 3 pp. http://www.omicsonline.com/open-access/orthogonal-matrix-invariants-1736-4337-S1-007.php?aid=60212
7.
I.B. Kaygorodov, A.A. Lopatin, Yu.S. Popov, “Conservative algebras of 2-dimensional algebras”, Linear Algebra and its Applications, 486 (2015), 255-274 http://www.sciencedirect.com/science/article/pii/S0024379515004760
I.B. Kaygorodov, A.A. Lopatin, Yu.S. Popov, “Identities of sum of two PI-algebras in the case of positive characteristic”, International Journal of Algebra and Computation, 25:8 (2015), 1265-1273 http://www.worldscientific.com/doi/abs/10.1142/S021819671550040X
A.A. Lopatin, I.P. Shestakov, “Associative nil-algebras over finite fields”, International J. of Algebra and Computation, 23:8 (2013), 1881–1894 http://www.worldscientific.com/doi/abs/10.1142/S0218196713500471