A superrank of varieties of Lie algebras

被引：0
|
作者：
M. V. Zaitsev
机构：
来源：
Algebra and Logic | 1998年 / 37卷 / 4期
关键词：
Homogeneous Element; Monomial Identity; Standard Identity; Multilinear Polynomial; Nontrivial Identity;
D O I：
10.1007/BF02671626
中图分类号：
学科分类号：
摘要：
A variety of Lie algebras over a field of characteristic 0 has a finite superrank if it is generated by the Grassmann envelope of a finitely generated Lie superalgebra. We prove that every commutator variety not in NcA has infinite superrank. Consequently, infinite are superranks of all polynilpotent varieties of Lie algebras except Nc and NcA.
引用
收藏
页码：223 / 233
页数：10
相关论文
共 50 条
  • [31] Automorphic equivalence in the varieties of representations of Lie algebras
    Tsurkov, A.
    COMMUNICATIONS IN ALGEBRA, 2020, 48 (01) : 397 - 409
  • [32] COMPLEXITY OF VARIETIES OF LIE-ALGEBRAS AND OF THEIR REPRESENTATIONS
    RAZMYSLOV, YP
    VESTNIK MOSKOVSKOGO UNIVERSITETA SERIYA 1 MATEMATIKA MEKHANIKA, 1988, (04): : 75 - 78
  • [33] LOCALLY REPRESENTABLE VARIETIES OF LIE-ALGEBRAS
    ZAITSEV, MV
    MATHEMATICS OF THE USSR-SBORNIK, 1990, 67 (01): : 249 - 259
  • [34] VARIETIES OF RESIDUALLY FINITE LIE-ALGEBRAS
    PREMET, AA
    SEMENOV, KN
    MATHEMATICS OF THE USSR-SBORNIK, 1988, 137 (1-2): : 109 - 118
  • [35] JACOBI VARIETIES AND ASSOCIATED LIE-ALGEBRAS
    LICHNEROWICZ, A
    JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 1978, 57 (04): : 453 - 488
  • [36] Specht property of varieties of graded Lie algebras
    Correa, Daniela Martinez
    Koshlukov, Plamen
    MONATSHEFTE FUR MATHEMATIK, 2023, 202 (01): : 65 - 92
  • [37] SCHREIER VARIETIES OF N-LIE ALGEBRAS
    KHASHINA, YA
    SIBERIAN MATHEMATICAL JOURNAL, 1991, 32 (02) : 348 - 349
  • [38] SOME FINITE VARIETIES OF LIE-ALGEBRAS
    MONEYHUN, K
    STITZINGER, E
    JOURNAL OF ALGEBRA, 1991, 143 (01) : 173 - 178
  • [39] SUPPORT VARIETIES FOR RESTRICTED LIE-ALGEBRAS
    FRIEDLANDER, EM
    PARSHALL, BJ
    INVENTIONES MATHEMATICAE, 1986, 86 (03) : 553 - 562
  • [40] Zassenhaus varieties of general linear Lie algebras
    Premet, A
    Tange, R
    JOURNAL OF ALGEBRA, 2005, 294 (01) : 177 - 195
12345