Pasha Zusmanovich

... 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.

Pasha Zusmanovich

[writings] [soft] [teaching] [seminar] [for students] [talks] [links & files]

papers and manuscripts

The versions of the texts posted here (if any) are preferrred over the published ones, as they usually incorporate minor mathematical, typographical, and linguistic corrections. arXiv versions are not updated anymore.

[43] (with Arezoo Zohrabi) A \(\delta\)-first Whitehead Lemma for Jordan algebras, Communications in Mathematics 33 (2025), no.1, Paper no.2

[42] A variant of Baer's theorem, Rocky Mountain Journal of Mathematics 54 (2024), no.3, 929-932

[41] Mathematicians going east, Journal of Humanistic Mathematics 14 (2024), no.1, 114-167

[40] When Hom-Lie structures form a Jordan algebra, Journal of Algebra and Its Applications 22 (2023), no.9, 2350197; arXiv:2211.06631 [Zentralblatt]

[39] On contact brackets on the tensor product, Linear and Multilinear Algebra 70 (2022), no.19, 4695-4706; arXiv:2211.06638 [Zentralblatt]

[38] On the utility of Robinson-Amitsur ultrafilters. III, Periodica Mathematica Hungarica 85 (2022), no.2, 399-404; arXiv:2211.06633 [Zentralblatt]

[37] (with Alexander Grishkov, Henrique Guzzo Jr., and Marina Rasskazova) On simple 15-dimensional Lie algebras in characteristic 2, Journal of Algebra 593 (2022), 295-318 [Zentralblatt]

Accompanying GAP code

[36] (with Viktor Lopatkin) Commutative Lie algebras and commutative cohomology in characteristic 2, Communications in Contemporary Mathematics 23 (2021), no.5, 2050046 [Zentralblatt]

[35] (with Arezoo Zohrabi) On Hermitian and skew-Hermitian matrix algebras over octonions, Journal of Nonlinear Mathematical Physics 28 (2021), no.1, 108-122 [Zentralblatt]

GAP code for constructing those algebras (not mentioned in the paper)

[34] On regular Lie algebras, Communications in Algebra 49 (2021),no.3, 1104-1119; arXiv:2211.06640 [Zentralblatt]

[33] (with Arezoo Zohrabi) A \(\delta\)-first Whitehead Lemma, Journal of Algebra 573 (2021), 476-491; arXiv:2211.06645 [Zentralblatt]

[32] (with Ivan Kaygorodov) On anticommutative algebras for which \([R_a,R_b]\) is a derivation, Journal of Geometry and Physics 163 (2021), 104113 [Zentralbatt]

[31] (with Abdenacer Makhlouf) Ado theorem for nilpotent Hom-Lie algebras, International Journal of Algebra and Computation 29 (2019), no.7, 1343-1365; arXiv:1807.10944 [Zentralblatt]

[30] (with Dietrich Burde) Commutative post-Lie algebra structures on Kac-Moody algebras, Communications in Algebra 47 (2019), no.12, 5218-5226; arXiv:1805.04267 [Zentralblatt]

[29] On Lie p-algebras of cohomological dimension one, Indagationes Mathematicae 30 (2019), no.2, 288-299; arXiv:1601.00352 [Zentralblatt]

[28] (with Abdenacer Makhlouf) Hom-Lie structures on Kac-Moody algebras, Journal of Algebra 515 (2018), 278-297; arXiv:1805.00187 [Zentralblatt]

[27] Non-semigroup gradings of associative algebras, Linear Algebra and its Applications 523 (2017), 52-58; arXiv:1609.03924 [Zentralblatt]

[26] Special and exceptional mock-Lie algebras, Linear Algebra and its Applications 518 (2017), 79-96 [Zentralblatt]

Albert program used in the paper

[25] (with Alexander Grishkov) Deformations of current Lie algebras. I. Small algebras in characteristic 2, Journal of Algebra 473 (2017), 513-544 [Zentralblatt]

[24] On the last question of Stefan Banach, Expositiones Mathematicae 34 (2016), no.4, 454-466; arXiv:1408.2982 [Zentralblatt]

[23] Lie algebras and around: selected questions, Matematicheskii Zhurnal (Almaty) 16 (2016), no.2 (A.S. Dzhumadil'daev Festschrift), 231-245; arXiv:1608.05863 [Zentralblatt]

[22] On the utility of Robinson-Amitsur ultrafilters. II, Journal of Algebra 466 (2016), 370-377 [Zentralblatt]

[21] Yet another proof of the Ado theorem, Journal of Lie Theory 26 (2016), no.3, 673-681; arXiv:1507.02233 [Zentralblatt]

[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.

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 [Zentralblatt]

[18] On near and the nearest correlation matrix, Journal of Nonlinear Mathematical Physics 20 (2013), no.3, 431-439 [Zentralblatt]

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

[16] A compendium of Lie structures on tensor products, Zapiski Nauchnykh Seminarov POMI 414 (2013) (N.A. Vavilov Festschrift), 40-81 [POMI] [mathnet.ru] = Journal of Mathematical Sciences 199 (2014), no.3, 266-288 [Zentralblatt]

[15] On the utility of Robinson-Amitsur ultrafilters, Journal of Algebra 388 (2013), 268-286; arXiv:0911.5414 [Zentralblatt]

[14] How Euler would compute the Euler-Poincaré characteristic of a Lie superalgebra, Expositiones Mathematicae 29 (2011), no.3, 345-360 [Zentralblatt]

[13] (with Askar Dzhumadil'daev) The alternative operad is not Koszul, Experimental Mathematics 20 (2011), no.2, 138-144 [Project Euclid] [Taylor & Francis] [Zentralblatt]

Corrigendum: 21 (2012), no.4, 418 [Project Euclid] [Taylor & Francis]

Albert program used in the paper

[12] Nonexistence of invariant symmetric forms on generalized Jacobson-Witt algebras revisited, Communications in Algebra 39 (2011), no.2, 548-554; arXiv:0902.0038 [Zentralblatt]

[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 [Taylor & Francis] [World Scientific] [Atlantis Press]; arXiv:0901.1395 [Zentralblatt]

[10] On δ-derivations of Lie algebras and superalgebras, Journal of Algebra 324 (2010), no.12, 3470-3486 [Zentralblatt]

Erratum: 410 (2014), 545-546 [Zentralblatt]

Accompanying GAP code

[9] (with Askar Dzhumadil'daev) Commutative 2-cocycles on Lie algebras, Journal of Algebra 324 (2010), no.4, 732-748 [Zentralblatt]

Accompanying GAP code

[8] ω-Lie algebras, Journal of Geometry and Physics 60 (2010), no.6-8, 1028-1044 [Zentralblatt]

Accompanying GAP code

[7] A converse to the Whitehead Theorem, Journal of Lie Theory 18 (2008), no.4, 811-815; arXiv:0808.0212 [Zentralblatt]

[6] A converse to the Second Whitehead Lemma, Journal of Lie Theory 18 (2008), no.2, 295-299 [Zentralblatt]

Erratum: 24 (2014), no.4, 1207-1208 [Zentralblatt]

[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 [Zentralblatt]

[4] Deformations of W₁(n) ⊗ A and modular semisimple Lie algebras with a solvable maximal subalgebra, Journal of Algebra 268 (2003), no.2, 603-635 [Zenralblatt]

[3] The second homology group of current Lie algebras, K-Theory (ed. C. Kassel et al.), Astérisque 226 (1994), 435-452 [Numdam] [SMF] [Zentralblatt]

[2] Central extensions of current algebras, Transactions of the American Mathematical Society 334 (1992), no.1, 143-152 [AMS] [JSTOR] [Zentralblatt]; Erratum and addendum: 362 (2010), no.10, 5601-5603 [AMS] [JSTOR] [Zentralblatt]; arXiv:0812.2625.

[1] A Lie algebra that can be written as a sum of two nilpotent subalgebras, is solvable, Mathematical Notes 50 (1991), no.3, 909-912; arXiv:0911.5418 [Zentralblatt] Russian original

non-math papers

(with L.A. Bokut et al.) Askar Serkulovich Dzhumadil'daev (on his 60th birthday), Russian Mathematical Surveys 72 (2017), no.4, 199-202 [Zentralblatt]

Russian original
(with A. Kong et al.) Detection of sharing by descent, long-range phasing and haplotype imputation, Nature Genetics 40 (2008), no.9, 1068-1075

(with D. Gudbjartsson et al.) Many sequence variants affecting diversity of adult human height, Nature Genetics 40 (2008), no.5, 609-615

(some) questions

A question - Lie-algebraic monster (partially in Russian).
Lie algebras that can be written as the sum of two nilpotent subalgebras.
Leites' (super)questions.
Grishkov's characteristic 2 questions.

other bits and pieces

Zentralblatt reviews
In 1993-1995 and 2002-2020 I was a reviewer for Mathematical Reviews. Old reviews: 2009-June 2011

till 2008

My mathematical genealogy:

Created: Sat Jan 20 2001
Last modified: Sat Oct 12 07:02:14 CEST 2024