Mathematics and Statistics Vol. 11(3), pp. 598 - 606
DOI: 10.13189/ms.2023.110318
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Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras

I.S. Rakhimov ^*
Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA (UiTM), Malaysia

ABSTRACT

In the paper, we propose three isomorphism criteria for a subclass of finite-dimensional Leibniz algebras. Isomorphism Criterion 1 has been given earlier (see [5]). We introduce notations for new structure constants. Using the new notation, we state the isomorphism criterion 2. To formulate Isomorphism Criterion 3, we introduce "semi-invariant functions" needed. We prove that these three Isomorphism Criteria are equivalent. The isomorphism criterion 3 is convenient to find the invariant functions to represent isomorphism classes. The proof of the isomorphism criteria in the general case is computational and is based on hypothetic convolution identities given in [11]. Therefore, we give details in the ten-dimensional case.

KEYWORDS
Leibniz Algebra, Isomorphism Criterion, Adapted Basis

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] I.S. Rakhimov , "Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras," Mathematics and Statistics, Vol. 11, No. 3, pp. 598 - 606, 2023. DOI: 10.13189/ms.2023.110318.

(b). APA Format:
I.S. Rakhimov (2023). Isomorphism Criteria for A Subclass of Filiform Leibniz Algebras. Mathematics and Statistics, 11(3), 598 - 606. DOI: 10.13189/ms.2023.110318.