|
... 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 Л. Пантелееву, 10 августа 1932 г.
|
[versions of texts posted here are newer than those in arXiv]
publications
[11] Invariants of Lie algebras extended over commutative algebras without unit, J. Nonlin. Math. Phys., to appear; arXiv:0901.1395.
[10] Non-existence of invariant symmetric forms on generalized Jacobson-Witt algebras revisited, Comm. Algebra, to appear; arXiv:0902.0038.
[9] (with Askar Dzhumadil'daev) Commutative 2-cocycles on Lie algebras, J. Algebra 324 (2010), 732-748; arXiv:0907.4780. ←
[accompanying GAP code]
[8] ω-Lie algebras, J. Geom. Phys. 60 (2010), 1028-1044; arXiv:0812.0080. [accompanying GAP code]
[7] A converse to the Whitehead Theorem, J. Lie Theory 18 (2008), 811-815; arXiv:0808.0212.
[6] A converse to the Second Whitehead Lemma, J. 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, Lin. Algebra Appl. 407 (2005), 71-104; arXiv:math/0302334.
[4] Deformations of W1(n) ⊗ A and modular semisimple Lie algebras with a solvable maximal subalgebra, J. Algebra 268 (2003), 603-635; arXiv:math/0204004.
[3] The second homology group of current Lie algebras, Astérisque 226 (1994), 435-452; arXiv:0808.0217.
[2] Central extensions of current algebras, Trans. Amer. Math. Soc. 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, Math. Notes 50 (1991), 909-912; arXiv:0911.5418. [Russian original]
Offprints of items 1 and 4-7 will be gladly provided upon request to any collector of dead trees, as I don't know what to do with them.
manuscripts
[*] How Euler would compute the Euler-Poincaré characteristic of a Lie superalgebra, arXiv:0812.2255.
[*] (with Askar Dzhumadil'daev) The alternative operad is not Koszul, arXiv:0906.1272. ←
[Albert program used in it]
[corresponding OEIS entries:
A161391,
A161392,
A161393]
[*] On δ-derivations of Lie algebras and superalgebras, arXiv:0907.2034. ←
[accompanying GAP code]
[*] On the utility of Robinson-Amitsur ultrafilters, arXiv:0911.5414.
bits and pieces
[#] Cohomology of algebras (synopsis of lectures at South China Normal Univ., May-June 2010).
[#] Low-dimensional cohomology of current Lie algebras (talk at Mathematics colloquium at Univ. of Iceland, September 2009).
[#] Questions on Lie algebras of cohomological dimension 1 (last revised September 2009).
[#] Lie algebras that can be written as the sum of two nilpotent subalgebras (last revised September 2008).
[#] Maximum likelihood and EM algorithm (talk at Statistics colloquium at Univ. of Iceland, March 2007).
[#] Leites' (super)questions (last revised January 2005).
[#] A question - Lie-algebraic monster (June 2004; in Russian).
[#] On minimal nonabelian Lie algebras of characteristic zero (in Russian; an ancient (circa 1986) note published in some collection of students' works) [1] [2] [3] [4] [5]
reviews
Mathematical Reviews (as of January 2010)
Zentralblatt