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... написал два трактата о числах. Ими доволен вполне. Удалось вывести две теоремы,
потом опровергнуть их, потом опровергнуть опровержение, а потом снова опровергнуть.
На этом основании удалось вывести еще две теоремы... Выводы оказались столь
неожиданные, что я, благодаря им, стал сильно смахивать на естественного мыслителя.
Да вдобавок еще естественного мыслителя из города Курска. Скоро мне будет как раз к лицу
заниматься квадратурой круга или трисекцией угла.
Деятельность малограмотного ученого всегда была мне приятна. Но тут это становится опасным. Д. Хармс, из
письма к А.И. Пантелееву,
10 августа 1932 г.
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publications
[arXiv] [MR entries] [Zentralblatt entries] [google scholar][14] How Euler would compute the Euler-Poincaré characteristic of a Lie superalgebra, Expositiones Mathematicae 29 (2011), 345-360; arXiv:0812.2255.
[13] (with Askar Dzhumadil'daev) The alternative operad is not Koszul, Experimental Mathematics 20 (2011), 138-144.
[12] Non-existence of invariant symmetric forms on generalized Jacobson-Witt algebras revisited, Communications in Algebra 39 (2011), 548-554; arXiv:0902.0038.
[11] Invariants of Lie algebras extended over commutative algebras without unit, Journal of Nonlinear Mathematical Physics 17 (2010), Suppl. 1 (special issue in memory of F.A. Berezin), 87-102; arXiv:0901.1395.
[10] On δ-derivations of Lie algebras and superalgebras, Journal of Algebra 324 (2010), 3470-3486; arXiv:0907.2034. [accompanying GAP code]
[9] (with Askar Dzhumadil'daev) Commutative 2-cocycles on Lie algebras, Journal of Algebra 324 (2010), 732-748; arXiv:0907.4780. [accompanying GAP code]
[8] ω-Lie algebras, Journal of Geometry and Physics 60 (2010), 1028-1044; arXiv:0812.0080. [accompanying GAP code]
[7] A converse to the Whitehead Theorem, Journal of Lie Theory 18 (2008), 811-815; arXiv:0808.0212.
[6] A converse to the Second Whitehead Lemma, Journal of Lie Theory 18 (2008), 295-299; arXiv:0704.3864.
[5] Low-dimensional cohomology of current Lie algebras and analogs of the Riemann tensor for loop manifolds, Linear Algebra and its Applications 407 (2005), 71-104; arXiv:math/0302334.
[4] Deformations of W1(n) ⊗ A and modular semisimple Lie algebras with a solvable maximal subalgebra, Journal of Algebra 268 (2003), 603-635; arXiv:math/0204004.
[3] The second homology group of current Lie algebras, K-Theory (ed. C. Kassel et al.), Astérisque 226 (1994), 435-452; arXiv:0808.0217.
[2] Central extensions of current algebras, Transactions of the American Mathematical Society 334 (1992), 143-152; Erratum and addendum: 362 (2010), 5601-5603; arXiv:0812.2625.
[1] A Lie algebra that can be written as a sum of two nilpotent subalgebras, is solvable, Mathematical Notes 50 (1991), 909-912; arXiv:0911.5418. [Russian original]
Offprints of items [4],[5],[7],[10] will be gladly provided upon request to any collector of dead trees, as I don't know what to do with them.
manuscripts
[*] On the utility of Robinson-Amitsur ultrafilters, arXiv:0911.5414.[*] Lie algebras with given properties of subalgebras and elements, arXiv:1105.4284.
[*] (with Fedor Petrov) On Shirshov bases of graded algebras, arXiv:1201.5837.
[*] On near(est) correlation matrix.
talks
[some of them listed together with writings above][#] A commutative 2-cocycles approach to classification of simple Novikov algebras (talk at the conference Non-Associative Algebras and Related Topics, Coimbra, July 2011).
[#] Novikov structures on Kac-Moody and modular semisimple Lie algebras (talk at the IVth workshop Discrete Groups and Geometric Structures with Applications, Oostende, May 2011).
[#] Cohomology of current algebras (talk at St. Petersburg algebraic seminar at POMI, April 2011).
[#] Converse second and third Whitehead lemmata (abstract of talk at the 2nd workshop Lie Algebras, Algebraic Groups and Invariant Theory, Moscow, January 2011; in Russian).
[#] Low-dimensional cohomology of current Lie algebras (talk at Mathematics colloquium at Univ. of Iceland, September 2009).
[#] Maximum likelihood and EM algorithm (talk at Statistics colloquium at Univ. of Iceland, March 2007).
other bits and pieces
[!] Nijenhuis tensor, R-matrix, Saletan contractions, and all that (October 2007).[!] mathoverflow
[!] OEIS: A192211, A192212, etc.
reviews
Mathematical Reviews: 2009-June 2011
till 2008
Zentralblatt: as of November 2011
questions
teaching
[+] Methods of Mathematical Physics, Tallinn Univ. Technology, Fall 2011.[+] Cohomology of algebras (synopsis of lectures), South China Normal Univ., Summer 2010.