On properties of some nilpotent evolution algebras and their enveloping algebras

被引：1
作者：
Alarafeen, Ahmad [1 ]
Ahmad, Azhana [1 ]
Qaralleh, Izzat [2 ]
机构：
[1] Univ Sains Malaysia, Sch Math Sci, Usm 11800, Penang, Malaysia
[2] Tafila Tech Univ, Fac Sci, Dept Math, Tafila, Jordan
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2023年 / 22卷 / 12期
关键词：
Evolution algebra; nilpotent; derivation; enveloping algebras;
D O I：
10.1142/S0219498823502596
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider n-dimensional nilpotent finite-dimensional evolution algebras with non-maximal index of nilpotency. We give complete invariants of these algebras in order to classify them. Then, we describe their associative enveloping algebras. We also give a positive answer to the question whether a derivation of this nilpotent evolution algebra is possible to be extended to its enveloping algebra.
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页数：20
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共 12 条
  • [1] Properties of nilpotent evolution algebras with no maximal nilindex
    Alarfeen, Ahmad
    Qaralleh, Izzat
    Ahmad, Azhana
    [J]. EUROPEAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2021, 14 (01): : 278 - 300
  • [2] Classification of three-dimensional evolution algebras
    Cabrera Casado, Yolanda
    Siles Molina, Mercedes
    Victoria Velasco, M.
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2017, 524 : 68 - 108
  • [3] SOME PROPERTIES OF EVOLUTION ALGEBRAS
    Camacho, L. M.
    Gomez, J. R.
    Omirov, B. A.
    Turdibaev, R. M.
    [J]. BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2013, 50 (05) : 1481 - 1494
  • [4] The derivations of some evolution algebras
    Camacho, L. M.
    Gomez, J. R.
    Omirov, B. A.
    Turdibaev, R. M.
    [J]. LINEAR & MULTILINEAR ALGEBRA, 2013, 61 (03) : 309 - 322
  • [5] On Evolution Algebras
    Casas, J. M.
    Ladra, M.
    Omirov, B. A.
    Rozikov, U. A.
    [J]. ALGEBRA COLLOQUIUM, 2014, 21 (02) : 331 - 342
  • [6] On nilpotent evolution algebras
    Elduque, Alberto
    Labra, Alicia
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2016, 505 : 11 - 31
  • [7] Nilpotent evolution algebras over arbitrary fields
    Hegazi, A. S.
    Abdelwahab, Han
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 486 : 345 - 360
  • [8] Mukhamedov F., 2016, INT J ALGEBRA, V10, P327
  • [9] On S-Evolution Algebras and Their Enveloping Algebras
    Mukhamedov, Farrukh
    Qaralleh, Izzat
    [J]. MATHEMATICS, 2021, 9 (11)
  • [10] Classification of nilpotent evolution algebras and extensions of their derivations
    Mukhamedov, Farrukh
    Khakimov, Otabek
    Qaralleh, Izzat
    [J]. COMMUNICATIONS IN ALGEBRA, 2020, 48 (10) : 4155 - 4169
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