Geodesic
Non-alternating Hamiltonian forms over a divided power algebra in characteristic~$2$
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2023), pp. 95-100.

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A classification of nonalternating Hamiltonian forms with coefficients in a divided power algebra over a perfect field $K$ of characteristic $2$ is given. A description of the corresponding simple Lie algebras are found. A complete system of invariants of nonalternating symmetric bilinear forms over $K$ is constructed.
Keywords: field of characteristic $2$, non-alternating Hamiltonian form, Lie algebra. 
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A. V. Kondratieva; M. I. Kuznetsov. Non-alternating Hamiltonian forms over a divided power algebra in characteristic~$2$. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2023), pp. 95-100. http://geodesic.mathdoc.fr/item/IVM_2023_6_a8/

[1] Lin Lei, “Non-alternating hamiltonian algebra $P(n,m)$ of characteristic two”, Commun. in Algebra, 21:2 (1993), 399–411 | DOI | MR | Zbl

[2] Kaplansky I., “Some simple Lie algebras of characteristic $2$”, Lect. Notes Math., 933, 1982, 127–129 | DOI | MR | Zbl

[3] Bouarroudj S., Grozman P., Lebedev A., Leites D., “Divided power $($co$)$homology. Presentation of simple finite dimensional modular superalgebras with Cartan matrix”, Homology, Homotopy Appl., 12:1 (2010), 237–248 | DOI | MR

[4] Lebedev A., “Analog of the ortogonal, Hamiltonian, Poisson, and contact Lie superalgebras in characteristic $2$”, J. Nonlin. Math. Phys., 17:1 (2010), 217–251 | MR | Zbl

[5] Kuznetsov M. I., Kondrateva A. V., Chebochko N. G., “O gamiltonovykh algebrakh Li kharakteristiki $2$”, Matem. zhurnal, 16:2 (2016), 54–65 http://www.math.kz | Zbl

[6] Kats V. G., “Opisanie filtrovannykh algebr Li, s kotorymi assotsiirovany graduirovannye algebry Li kartanovskogo tipa”, Izv. AN SSSR, Ser. Matem., 38:4 (1974), 800–834

[7] Kuznetsov M. I., Kirillov S. A., “Gamiltonovy differentsialnye formy nad algebroi srezannykh mnogochlenov”, UMN, 41:2 (1986), 197–198 | MR | Zbl

[8] Benkart G. M., Gregory T. B., Osborn J. M., Strade H., Wilson R. L., “Isomorphism classes of Hamiltonian Lie algebras” (Madison 1987), Lect. Notes Math., 1373, 1989, 42–57 | DOI | MR | Zbl

[9] Skryabin S. M., Kanonicheskii vid gamiltonovykh i kontaktnykh form nad algebrami razdelennykh stepenei, Dep. v VINITI, 8594-B86, 1986

[10] Skryabin S. M., “Klassifikatsiya gamiltonovykh form nad algebrami razdelennykh stepenei”, Matem. sb., 181:1 (1990), 114–133

[11] Kondrateva A. V., “Non-Alternating Hamiltonian Lie Algebras of Characteristics Two in Three Variables”, Lobachevskii J. Math., 42:12 (2021), 2841–2853 | DOI | MR | Zbl

[12] Kostrikin A. I., Shafarevich I. R., “Graduirovannye algebry Li konechnoi kharakteristiki”, Izv. AN SSSR. Ser. matem., 33:2 (1969), 251–322

[13] Strade H., Simple Lie algebras over fields of positive characteristic. I: Structure theory, de Gruyter Expositions in Math., De Gruyter, Berlin, 2004 | MR | Zbl

[14] Krylyuk Ya. S., O neprivodimykh moduyalkh algebr Li kartanovskogo tipa v konechnoi kharakteristike, ch. I, II, III, Dep. v VINITI, 3863–78, M., 1978; Деп. в ВИНИТИ, 3864–78; Деп. в ВИНИТИ, 3865–78

[15] Khodzh V., Pido D., Metody algebraicheskoi geometrii, v. 1, Izd-vo in. lit., M., 1954