Pasha Zusmanovich's math stuff [math links] [contact info] [search

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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.


Versions of texts posted here (if any) are newer than those in arXiv; arXiv versions usually incorporate minor mathematical, typographical and linguistic corrections as compared with the published ones.

[MR entries] [Zentralblatt entries]

[22]   (with Alexander Grishkov) Deformations of current Lie algebras. I. Small algebras in characteristic 2, arXiv:1410.3645.

[21]   On the last question of Stefan Banach, arXiv:1408.2982.   [accompanying Perl code]

[20]   (with Hayk Melikyan) Melikyan algebra is a deformation of a Poisson algebra, Journal of Physics: Conference Series 532 (2014), 012019.

[19]   Lie algebras with given properties of subalgebras and elements, Algebra, Geometry and Mathematical Physics (ed. A. Makhlouf et al.), Springer Proceedings in Mathematics & Statistics 85 (2014), 99-109; arXiv:1105.4284.

[18]   On near and the nearest correlation matrix, Journal of Nonlinear Mathematical Physics 20 (2013), 431-439; arXiv:1303.3226.

[17]   (with Fedor Petrov) On Shirshov bases of graded algebras, Israel Journal of Mathematics 197 (2013), 23-28; arXiv:1201.5837.

[16]   A compendium of Lie structures on tensor products, Zapiski Nauchnykh Seminarov POMI 414 (2013) (N.A. Vavilov Festschrift), 40-81 [] [] = Journal of Mathematical Sciences 199 (2014), 266-288; arXiv:1303.3231.

[15]   On the utility of Robinson-Amitsur ultrafilters, Journal of Algebra 388 (2013), 268-286.

[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; Corrigendum: 21 (2012), 418.

[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;   Erratum: 410 (2014), 545-546; 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; Erratum: 24 (2014), 1207-1208; 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]

genetics/statistics papers

[α]   (with A. Kong et al.) Detection of sharing by descent, long-range phasing and haplotype imputation, Nature Genetics 40 (2008), 1068-1075.
[β]   (with D. Gudbjartsson et al.) Many sequence variants affecting diversity of adult human height, Nature Genetics 40 (2008), 609-615.

slides of (some) talks

other bits and pieces

Nijenhuis tensor, R-matrix, Saletan contractions, and all that (October 2007).
OEIS entries


Mathematical Reviews:   2009-June 2011    till 2008
Zentralblatt:   as of November 2011

(some) questions


NCCU, Fall 2013.
Methods of Mathematical Physics, Tallinn Univ. Technology, Fall 2011.
Cohomology of algebras (synopsis of lectures), South China Normal Univ., Summer 2010.

created Jan 20 2001
last modified Fri Jul 3 13:36:42 CEST 2015