Pasha Zusmanovich

[math stuff] [teaching] [topics for students] [travel] [links, files, etc.]
... 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.
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, in their turn, usually incorporate minor mathematical, typographical and linguistic corrections as compared with the published ones.

[Math Reviews entries] [Zentralblatt entries]

[24]   On the utility of Robinson-Amitsur ultrafilters. II, arXiv:1508.07496. pdf TeX

[23]   Yet another proof of the Ado theorem, arXiv:1507.02233.

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

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

[20]   (with Hayk Melikyan) Melikyan algebra is a deformation of a Poisson algebra, 3Quantum: Algebra Geometry Information (ed. E. Paal et al.), Journal of Physics: Conference Series 532 (2014), 012019; arXiv:1401.2566.   [accompanying GAP code]

[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 [POMI] [] = 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; arXiv:0911.5414.

[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 [Project Euclid] [Taylor & Francis]   Corrigendum: 21 (2012), 418 [Project Euclid] [Taylor & Francis]; arXiv:0906.1272   Extended abstract to Polynomial Computer Algebra '2011: pdf TeX   [Albert program used in the paper]

[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.

  [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   Abstract to the 2nd Workshop "Lie Algebras, Algebraic Groups and Invariant Theory" (Moscow, January 2011) (in Russian)   pdf

  [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. pdf
[β]   (with D. Gudbjartsson et al.) Many sequence variants affecting diversity of adult human height, Nature Genetics 40 (2008), 609-615. pdf

slides of (some) talks

other bits and pieces

OEIS entries
reviews:   Math Reviews: 2009-June 2011 pdf till 2008 pdf   Zentralblatt: as of November 2011 pdf

(some) questions

  1. A question - Lie-algebraic monster (last updated August 10, 2011; partially in Russian).
  2. Lie algebras that can be written as the sum of two nilpotent subalgebras (last revised September 2011). pdf TeX
  3. Questions on Lie algebras of cohomological dimension 1 (last revised January 2015). pdf TeX
  4. Leites' (super)questions (last revised July 2012). pdf TeX

Created: Sat Jan 20 2001
Last modified: Sat Oct 3 12:34:52 CEST 2015