Lev Vasil'evich Sabinin (obituary)

Yu. E. Borovskii   ; V. A. Kudryavtsev   ; Yu. G. Reshetnyak

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 61 (2006) no. 5, pp. 975-980

Bibliographie

[1] “O geometrii subsimmetricheskix prostranstv”, Nauchn. dokl. vyssh. shkoly. Ser. fiz.-matem. nauk, 3 (1958), 46–49

[2] “O strukture grupp dvizhenii odnorodnyx rimanovyx prostranstv s osevoi simmetriei”, Nauchn. dokl. vyssh. shkoly. Ser. fiz.-matem. nauk, 6 (1958), 127–138 | Zbl

[3] Zerkalnye simmetrii rimanovyx prostranstv, Avtoreferat diss. ... kand. fiz.-matem. nauk, Izd-vo MGU, M., 1959

[4] “Geometriya odnorodnyx rimanovyx prostranstv i vnutrennyaya geometriya simmetricheskix prostranstv”, Dokl. AN SSSR, 129:6 (1959), 1238–1241 | MR | Zbl

[5] “O yavnom vyrazhenii form svyaznosti kvazisimmetricheskogo prostranstva cherez znacheniya tenzorov krivizny i krucheniya v nekotoroi tochke”, Dokl. AN SSSR, 132:6 (1960), 1273–1276 | MR | Zbl

[6] “O geometrii trisimmetricheskix rimanovyx prostranstv”, Sib. matem. zhurn., 2:2 (1961), 266–278 | MR | Zbl

[7] Lektsii po vysshei matematike, ch. 1, Novosibirskii gos. un-t, Novosibirsk, 1962

[8] Lektsii po vysshei matematike, ch. 2, Novosibirskii gos. un-t, Novosibirsk, 1963

[9] “Ob izoinvolyutivnyx razlozheniyax algebr Li”, Dokl. AN SSSR, 165:5 (1965), 1003–1006 | MR | Zbl

[10] “O glavnyx invomorfizmax algebr Li”, Dokl. AN SSSR, 175:1 (1967), 31–33 | MR | Zbl

[11] “Ob involyutivnyx summax algebr Li”, Tr. sem. vekt. tenz. anal., 14, 1968, 94–113 | MR | Zbl

[12] “Involyutivnaya dvoistvennost v prostyx kompaktnyx algebrax Li”, Tr. geometr. sem., 2, 1969, 277–298 | MR | Zbl

[13] “Glavnye invomorfizmy kompaktnyx algebr Li”, Tr. sem. vekt. tenz. anal., 15, 1970, 188–226 | MR | Zbl

[14] “O klassifikatsii trisimmetricheskix prostranstv”, Dokl. AN SSSR, 194:3 (1970), 518–520 | MR | Zbl

[15] “Odnorodnye rimanovy prostranstva s $(n-1)$-mernymi zerkalami”, Nekotorye kraevye zadachi obyknovennykh differentsialnyx uravnenii, Universitet druzhby narodov, M., 1970, 116–126 | MR

[16] Involyutivnaya geometriya algebr Li, Avtoreferat diss. ... dokt. fiz.-matem. nauk, Kazan. gos. un-t, Kazan, 1971

[17] “Trisimmetricheskie prostranstva s prostymi kompaktnymi gruppami dvizhenii”, Tr. sem. vekt. tenz. anal., 16, 1972, 202–226 | MR | Zbl

[18] “K ekvivalentnosti kategorii lup i odnorodnyx prostranstv”, Dokl. AN SSSR, 205:3 (1972), 533–536 | MR | Zbl

[19] “O geometrii lup”, Matem. zametki, 12:5 (1972), 605–616 | MR | Zbl

[20] “On the existence of half-Bol loops”, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.), 22:2 (1976), 147–148 (with B. L. Sharma) | MR | Zbl

[21] “Oduli kak novyi podxod k geometrii so svyaznostyu”, Dokl. AN SSSR, 233:5 (1977), 800–803 | MR | Zbl

[22] Osnovnye algebraicheskie struktury, Uchebnoe posobie, Universitet druzhby narodov, M., 1979 | Zbl

[23] Moduli, matritsy, formy, Uchebnoe posobie, Universitet druzhby narodov, M., 1981 | Zbl

[24] “Metody neassotsiativnoi algebry v differentsialnoi geometrii”, Dobavlenie k kn. (rus. izd.): Sh. Kobayasi, K. Nomidzu, Osnovy differentsialnoi geometrii, t. 1, Nauka, M., 1981, 293–339

[25] “O simmetricheskoi svyaznosti v prostranstve analiticheskoi lupy Mufang”, Dokl. AN SSSR, 262:4 (1982), 807–809 (with P. O. Mixeevym) | MR | Zbl

[26] Affinnaya ploskost, Uchebnoe posobie, Universitet druzhby narodov, M., 1982

[27] “O geometrii gladkix lup Bola”, Tkani i kvazigruppy, 1984, 144–154 (with P. O. Mixeevym) | MR | Zbl

[28] Ermitovy formy. Struktura endomorfizma, Uchebnoe posobie, Universitet druzhby narodov, M., 1984

[29] “O differentsialnoi geometrii lup Bola”, Doklady AN SSSR, 281:5 (1985), 1055–1057 (with P. O. Mixeevym) | MR | Zbl

[30] Teoriya gladkix lup Bola, Teksty lektsii, Universitet druzhby narodov, M., 1985 (with P. O. Mixeevym), (dvuyazychnoe posobie: na russkom i angliiskom yazykax) | MR | Zbl

[31] “Geometricheskie oduli”, Tkani i kvazigruppy, 1987, 88–98 | MR

[32] Endomorfizmy vektornyx prostranstv. Strukturnaya teoriya, Uchebnoe posobie, Universitet druzhby narodov, M., 1987

[33] “Ob infinitezimalnoi teorii lokalnyx analiticheskix lup”, Dokl. AN SSSR, 297:4 (1987), 801–804 (with P. O. Mixeevym)

[34] “O nelineinoi geometricheskoi algebre”, Tkani i kvazigruppy, 1988, 32–37 | MR

[35] “Differentsialnye uravneniya gladkix lup”, Tr. sem. vekt. tenz. anal., 23, 1988, 133–146 | MR | Zbl

[36] “Gladkie kvazigruppy i geometriya”, Itogi nauki i tekhniki. Problemy geometrii, 20, VINITI, M., 1988, 75–110 (with P. O. Mixeevym) | MR

[37] “Differentsialnaya geometriya i kvazigruppy”, Sovremennye problemy geometrii i analiza, Tr. In-ta matematiki SO AN SSSR, 14, Nauka, Novosibirsk, 1989, 208–221 | MR

[38] “Quasigroups and differential geometry”, Quasigroups and loops: theory and applications, Sigma Ser. Pure Math., 8, eds. O. Chein, H. Pflugfelder, J. D. H. Smith, Heldermann Verlag, Berlin, 1990, 357–430 (with P. O. Mikheev) | MR

[39] “O gladkix giporeduktivnyx lupax”, Dokl. AN SSSR, 314:3 (1990), 565–568 | Zbl

[40] “Quasigroups, geometry and physics”, Kvazigruppy i neassotsiativnye algebry v fizike, Eesti NSV Tead. Akad. Füüs. Inst. Uurim. (Tartu, 1989), 66, Tartu, Estonia, 1990, 24–53 | MR | Zbl

[41] Analiticheskie kvazigruppy i geometriya, Universitet druzhby narodov, M., 1991 | MR | Zbl

[42] “K teorii $\varphi$-prostranstv”, Tr. sem. vekt. tenz. anal., 24, 1991, 180–185 | MR | Zbl

[43] “Smooth quasigroups and Loops. New results”, Proceedings of the International Conference on Algebra, Dedicated to the memory of A. I. Malcev, Contemp. Math., 131, no. 1, eds. L. Bokut et al., Amer. Math. Soc., Providence, RI, 1992, 707–712 | MR

[44] “O zakone slozheniya skorostei v spetsialnoi teorii otnositelnosti”, UMN, 48:5 (1993), 183–184 (with P. O. Mixeevym) | MR | Zbl

[45] “O differentsialnyx uravneniyax gladkix lup”, UMN, 49:2 (1994), 165–166 | MR | Zbl

[46] “Pochti simmetricheskie i antisimmetricheskie prostranstva affinnoi svyaznosti”, Dokl. AN SSSR, 337:4 (1994), 454–455 (with P. O. Mixeevym) | Zbl

[47] “Geo-odular axiomatics of affine spaces”, Note Mat., 14:1 (1994), 109–113 | MR | Zbl

[48] “O girogruppax A. Ungara”, UMN, 50:5 (1995), 251–252 | MR | Zbl

[49] “Differentsialnye uravneniya geometricheskogo odulya”, Dokl. RAN, 344:6 (1995), 745–748 | MR | Zbl

[50] “On the theory of left $F$-quasigroups”, Algebras Groups Geom., 12:2 (1995), 127–137 (with L. L. Sabinina) | MR | Zbl

[51] “On the structure of $T,U,V$-isospins in theory of higher symmetry”, Vestn. RUDN. Ser. matem., 2:1 (1995), 130–134 | MR | Zbl

[52] “The theory of smooth hyporeductive and pseudoreductive loops”, Algebras Groups Geom., 13:1 (1996), 1–24 | MR | Zbl

[53] “Odnorodnye prostranstva i kvazigruppy”, Izv. vuzov. Ser. matem., 1996, no. 7, 77–84 | MR | Zbl

[54] “O diassotsiativnosti gladkix monoalternativngyx lup”, UMN, 51:4 (1996), 169–170 | MR | Zbl

[55] “Left quasigroups and reductive spaces”, Algebras Groups Geom., 13:4 (1996), 479–487 (with L. V. Sbitneva) | MR | Zbl

[56] “Ob infinitezimalnoi teorii reduktivnyx lup”, Dokl. RAN, 353:1 (1997), 26–28 | MR | Zbl

[57] “Smooth loops and Thomas precession”, Hadronic J., 20:3 (1997), 219–237 (with A. I. Nesterov) | MR | Zbl

[58] “Smooth loops, generalized coherent states, and geometric phases”, Internat. J. Theoret. Phys., 36:9 (1997), 1981–1989 (with A. I. Nesterov) | DOI | MR | Zbl

[59] Involyutivnaya geometriya algebr Li, RUDN, M., 1997

[60] “Undergraduate geometry: new approach”, Proceedings of 6-th International Symposium in Mathematics Education “Elfriede Wenzelburger” (UNAM, Mexico, 1997), Grupo Editorial Iberoamérica, Mexico, 1997, 161–164

[61] “On the notion of gyrogroup”, Aequationes Math., 56:1–2 (1998), 11–17 (with L. L. Sabinina, L. V. Sbitneva) | DOI | MR | Zbl

[62] “Quasigroups, geometry and nonlinear geometric algebra”, Acta Appl. Math., 50:1–2 (1998), 45–66 | DOI | MR | Zbl

[63] “Smooth loops, I”, Algebras Groups Geom., 15:2 (1998), 127–153 | MR | Zbl

[64] “Generalized Bol loops”, Vestn. RUDN. Ser. matem., 6:1 (1999), 182–190 (with C. Castillo) | Zbl

[65] “Perfect transsymmetric spaces”, Publ. Math. Debrecen, 54:3–4 (1999), 303–311 (with L. L. Sabinina, L. V. Sbitneva) | MR | Zbl

[66] “Methods of non-associative algebra in differential geometry”, Differential Geometry and Applications (Brno, 1998), Masaryk University, Brno, 1999, 419–427 | MR | Zbl

[67] Smooth quasigroups and loops, Math. Appl., 492, Kluwer, Dordrecht, 1999 | MR | Zbl

[68] “Smooth quasigroups and loops. Recent achievements and open problems”, Nonassociative algebra and its applications (São Paulo, 1998), Lecture Notes in Pure and Appl. Math., 211, eds. R. Costa et al., Dekker, New York, 2000, 337–344 | MR | Zbl

[69] “Non-associative geometry and discrete structure of space-time”, Comment. Math. Univ. Carol., 41:2 (2000), 347–357 (with A. I. Nesterov) | MR | Zbl

[70] “Smooth quasigroups and loops: forty-five years of incredible growth”, Comment. Math. Univ. Carol., 41:2 (2000), 377–400 | MR | Zbl

[71] “Nonassociative geometry: towards discrete structure of spacetime”, Phys. Rev. D (3), 62:8 (2000), 081501 (with A. I. Nesterov) | DOI | MR

[72] “Nonassociative geometry and discrete space-time”, Clifford algebras and their applications (Ixtapa, 1999), Internat. J. Theoret. Phys., 40:1 (2001), 351–358 | DOI | MR | Zbl

[73] “From symmetric to transsymmetric spaces”, 8th International Conference on Differential Geometry and Its Applications (Opava, 2001), Differential Geom. Appl., 17:2–3 (2002), 197–208, Elsevier, Amsterdam (with L. L. Sabinina, L. V. Sbitneva) | DOI | MR

[74] “Loop-theoretic foundations of differential geometry and relativity”, Webs quasigroups, Tver' State Univ., Tver', 2002, 67–72 | MR | Zbl

[75] Mirror geometry of Lie algebras, Lie groups and homogeneous spaces, Math. Appl., 573, Kluwer, Dordrecht, 2004 | MR | Zbl

[76] Nonassociative geometry: Friedmann–Robertson–Walker spacetime, (with A. I. Nesterov) arXiv: hep-th/0406229

[77] “Survey on smooth quasigroups development”, Non-associative algebra and its applications, Proceedings of V International Conference on Non-Associative Algebra and Its Applications (Oaxtepec, Mexico, 2003), Lecture Notes in Pure and Appl. Math., 246, eds. L. Sabinin, L. Sbitneva, I. Shestakov, Taylor Francis Group, CRC Press, Boca Raton, FL, 2006, 383–394 (with L. V. Sbitneva) | MR