01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Keywords:
Non-associative algebras and superalgebras.
Subject:
Non-associative algebraic stuctures
(Jordan algebras and superalgebras,
Lie algebras and superalgebras,
Malcev algebras and superalgebras,
Alternative algebras and superalgebras,
Structurable algebras and superalgebras,
Zinbiel algebras and superalgebras,
Leibniz algebras and superalgebras,
Terminal algebras and superalgebras,
Conservative algebras and superalgebras,
n-ary algebras and superalgebras,
Filippov algebras,
Poisson algebras and superalgebras and their generalizations;
derivations and generalized derivations,
automorphisms and generalized automorphisms,
Rota-Baxter operatos and other liner and non-linear mappings).
Main publications:
Ivan Kaygorodov & Yury Volkov, Complete classification of algebras of level two,
Moscow Mathematical Journal,19 (2019), 3, 485–521.
Ivan Kaygorodov & Yury Volkov, “The variety of 2-dimensional algebras over an algebraically closed field”,
Canadian Journal of Mathematics, 71 (2019), 4, 819–842.
Ivan Kaygorodov & Yury Popov, Split RegularHom-Leibniz Color 3-Algebras,
Colloquium Mathematicum,157 (2019), 2, 251–278.
Ivan Kaygorodov & Yury Popov, A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations,
Journal of Algebra, 456, (2016), 323–347.
Ivan Kaygorodov & Yury Popov, Generalized derivations of (color) n-ary algebras,
Linear and Multilinear Algebra, 64 (2016), 6, 1086–1106.
Ivan Kaygorodov, Yury Volkov, “The variety of 2-dimensional algebras over an algebraically closed field”, Canad. J. Math., 71:4 (2019), 819–842 , arXiv: 1701.08233
Patricia Damas Beites, Ivan Kaygorodov, Yury Popov, “Generalized derivations of multiplicative $n$-ary Hom-$\Omega$ color algebras”, Bulletin of the Malaysian Mathematical Sciences Society, 42:1 (2019), 315–335
Ilya B. Gorshkov, Ivan Kaygorodov, Alexey A. Kytmanov, Mohamed A. Salim, “The variety of nilpotent Tortkara algebras”, Zhurn. SFU. Ser. Matem. i fiz., 12:2 (2019), 173–184
Iqboljon Karimjanov, Ivan Kaygorodov & Abror Khudoyberdiyev, “The algebraic and geometric classification of nilpotent Novikov algebras”, J. Geom. Phys., 143 (2019), 11–21
Elisabete Barreiro, Ivan Kaygorodov & José M. Sánchez, “k-modules over linear spaces by n-linear maps admitting a multiplicative basis”, Algebr. Represent. Theory, 22:3 (2019), 615–626
Antonio Jesús Calderón, Ivan Kaygorodov & Paulo Saraiva, “Decompositions of linear spaces induced by n-linear maps”, Linear Multilinear Algebra, 67:6 (2019), 1250–1268
Ivan Kaygorodov, Alexander Pozhidaev & Paulo Saraiva, “On a ternary generalization of Jordan algebras”, Linear Multilinear Algebra, 67:6 (2019), 1074–1102
Antonio Jesús Calderón, Amir Fernández Ouaridi & Ivan Kaygorodov, “The classification of n-dimensional anticommutative algebras with (n−3)-dimensional annihilator”, Comm. Algebra, 47:1 (2019), 173–181
I. B. Gorshkov, I. B. Kaygorodov, A. V. Kukharev, A. A. Shlepkin, “On Thompson's conjecture for finite simple exceptional groups of Lie type”, Voprosy teorii predstavlenii algebr i grupp. 34, Zap. nauchn. sem. POMI, 478, POMI, SPb., 2019, 100–107
12.
Ivan Kaygorodov, Yuru Volkov, “Complete classification of algebras of level two”, Mosc. Math. J., 19:3 (2019), 485–521
Ivan Kaygorodov, Yury Popov, Alexander Pozhidaev, Yury Volkov, “Degenerations of Zinbiel and nilpotent Leibniz algebras”, Linear and Multilinear Algebra, 66:4 (2018), 704-716
Nurlan Ismailov, Ivan Kaygorodov, Yury Volkov, “The geometric classification of Leibniz algebras”, International Journal of Mathematics, 29:5 (2018), 1850035
Ivan Kaygorodov, Artem Lopatin, Yury Popov, “The structure of simple noncommutative Jordan superalgebras”, Mediterranean Journal of Mathematics, 15:2 (2018), 33
A. V. Kukharev, I. B. Kaygorodov, I. B. Gorshkov, “When the group ring of a simple finite group is serial”, J. Math. Sci. (N. Y.), 240:4 (2019), 481–493
23.
Ivan Kaygorodov, Yury Popov, “Commentary to Generalized derivations of Lie triple systems”, Open Mathematics, 2016, 543-544
Ivan Kaygorodov, Artem Lopatin, Yury Popov, “Conservative algebras of $2$-dimensional algebras”, Linear Algebra and its Applications, 486 (2015), 255-274 , arXiv: 1411.7744
Ivan Kaygorodov, “On (reverse) $(\alpha, \beta, \gamma)$-derivations of associative algebras”, Bollettino dell’Unione Matematica Italiana, 8:3 (2015), 181-187
26.
Ivan Kaygorodov, “Jordan $\delta$-derivations of associative algebras”, Journal of Generalized Lie Theory and Applications, s1 (2015), 003
27.
Ivan Kaygorodov, Elizaveta Okhapkina, “$\delta$-derivations of semisimple structurable algebras”, J. of Algebra and its Applications, 13:4 (2014), 1350130 (12 pages)
Ivan Kaygorodov, “$\delta$-Superderivations of Semisimple Finite-Dimensional Jordan Superalgebras”, Math. Notes, 91:2 (2012), 187–197
33.
Ivan Kaygorodov, “$\delta$-derivations of algebras and superalgebras”, Proceedings of the International Conference on Algebra 2010, Advances in Algebraic Structures (Gadjah Mada University, Indonesia, 7-10 October 2010), eds. W. Hemakul, S. Wahyuni, P. W. Sy, World Scientific Publishing Company, 2012, 374-380
34.
Ivan Kaygorodov, “On $\delta$-derivations of $n$-ary algebras”, Izv. Math., 76:6 (2012), 1150–1162
35.
Ivan Kaygorodov, Victor Zhelyabin, “$\delta$-superderivations of simple superalgebras of Jordan brackets”, St.-Peterburg Mathematical J., 23:4 (2012), 665-667
36.
Ivan Kaygorodov, “$(n+1)$-ary derivations of simple $n$-ary algebras”, Algebra and Logic, 50:5 (2011), 470–471
37.
I. B. Kaigorodov, “Ob obobschennom duble Kantora”, Vestnik Samarskogo gosudarstvennogo universiteta, 78:4 (2010), 42-50
Ivan Kaygorodov, “$\delta$-Superderivations of simple finite-dimensional Jordan and Lie superalgebras”, Algebra and Logic, 49:2 (2010), 130–144
39.
Ivan Kaygorodov, “$\delta$-derivations of classical Lie superalgebras”, Siberian Math. J., 50:3 (2009), 434–449
40.
Ivan Kaygorodov, “$\delta$-Derivations of simple finite-dimensional Jordan superalgebras”, Algebra and Logic, 46:5 (2007), 318–329
41.
I. B. Kaigorodov, “Nekotorye svoistva sverkhsovershennykh chisel”, Vestnik Kuzbasskogo Gosudarstvennogo Tekhnicheskogo Universiteta, 4:3 (2000), 90–93
ArXiv
42.
Ivan Kaygorodov, Yury Popov, Yury Volkov, “Degenerations of binary Lie and nilpotent Malcev algebras”, Communications in Algebra, 46:11 (2018), 4929-4941
43.
Ivan Kaygorodov, Yury Popov, A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations, Journal of Algebra, 456, 2016 , 323-347 pp., arXiv: 1506.00732
Ivan Kaygorodov, Artem Lopatin, Yury Popov, Identities of sum of two PI-algebras in the case of positive characteristic, 2015 , International Journal of Algebra and Computations, 25, 8, 1265-1273., arXiv: 1411.7395; ;
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