Novikov-Poisson algebras and associative commutative derivation algebras

被引：12
|
作者：
Zhelyabin, V. N. [1 ]
Tikhov, A. S. [2 ]
机构：
[1] Russian Acad Sci, Inst Math, Siberian Branch, Novosibirsk 630090, Russia
[2] Novosibirsk State Univ, Novosibirsk 630090, Russia
来源：
ALGEBRA AND LOGIC | 2008年 / 47卷 / 02期
基金：
俄罗斯基础研究基金会;
关键词：
Novikov algebra; Lie algebra; derivation algebra; Jordan superalgebra;
D O I：
10.1007/s10469-008-9002-4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe Novikov-Poisson algebras in which a Novikov algebra is not simple while its corresponding associative commutative derivation algebra is differentially simple. In particular, it is proved that a Novikov algebra is simple over a field of characteristic not 2 iff its associative commutative derivation algebra is differentially simple. The relationship is established between Novikov-Poisson algebras and Jordan superalgebras.
引用
收藏
页码：107 / 117
页数：11
相关论文
共 50 条
  • [1] Novikov-Poisson algebras and associative commutative derivation algebras
    V. N. Zhelyabin
    A. S. Tikhov
    [J]. Algebra and Logic, 2008, 47 : 107 - 117
  • [2] Embedding Novikov-Poisson algebras in Novikov-Poisson algebras of vector type
    Zakharov, A. S.
    [J]. ALGEBRA AND LOGIC, 2013, 52 (03) : 236 - 249
  • [3] Novikov-Poisson algebras
    Xu, XP
    [J]. JOURNAL OF ALGEBRA, 1997, 190 (02) : 253 - 279
  • [4] SIMPLE NOVIKOV-POISSON ALGEBRAS
    Zakharov, A. S.
    [J]. SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2023, 20 (02): : 1396 - 1404
  • [5] Algebraic Constructions for Novikov-Poisson Algebras
    Bao, Naping
    Hong, Yanyong
    [J]. MATHEMATICS, 2022, 10 (17)
  • [6] Transposed Poisson algebras, Novikov-Poisson algebras and 3-Lie algebras
    Bai, Chengming
    Bai, Ruipu
    Guo, Li
    Wu, Yong
    [J]. JOURNAL OF ALGEBRA, 2023, 632 : 535 - 566
  • [7] Some results on Novikov-Poisson algebras
    Zhao, YF
    Bai, CM
    Meng, DJ
    [J]. INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 2004, 43 (02) : 519 - 528
  • [8] Conformal Envelopes of Novikov-Poisson Algebras
    Kolesnikov, P. S.
    Nesterenko, A. A.
    [J]. SIBERIAN MATHEMATICAL JOURNAL, 2023, 64 (03) : 598 - 610
  • [9] NOVIKOV-POISSON ALGEBRAS AND SUPERALGEBRAS OF JORDAN BRACKETS
    Zakharov, Anton S.
    [J]. COMMUNICATIONS IN ALGEBRA, 2014, 42 (05) : 2285 - 2298
  • [10] Speciality of Jordan superalgebras related to Novikov-Poisson algebras
    V. N. Zhelyabin
    A. S. Zakharov
    [J]. Mathematical Notes, 2015, 97 : 341 - 348
12345