Local system of simple locally finite associative algebras
DOI:
https://doi.org/10.13069/jacodesmath.vi.242Keywords:
Local systems, Locally finite algebrasAbstract
In this paper, we study local systems of locally finite associative algebras over fields of free characteristic. We describe the perfect local systems and study the relation between them and theircorresponding locally finite associative algebras. $1$-perfect and conical local systems are also be considered and described briefly.
Accepted: 13 June 2024
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References
Y. Bahturin, A. A. Baranov, A. Zalesskii, Simple Lie subalgebras of locally finite associative algebras, Journal of Algebra 281(1) (2004) 225–246.
Y. Bahturin, H. Strade, Some examples of locally finite simple Lie algebras, Archiv der Mathematik 65(1) (1995) 23–26.
Y. Bakhturin, H. Strade, Locally finite-dimensional simple Lie algebras, Russian Academy of Sciences, Sbornik Mathematics 81(1) (1995) 137–161.
A. A. Baranov, Diagonal locally finite Lie algebras and a version of Ado’s theorem, Journal of Algebra 199(1) (1998) 1–39.
A. A. Baranov, Simple diagonal locally finite Lie algebras, Proceedings of the London Mathematical Society 77(2) (1998) 362–386.
A. A. Baranov, Classification of the direct limits of involution simple associative algebras and the corresponding dimension groups, Journal of Algebra 381(1) (2013) 73–95.
A. A. Baranov, Simple locally finite Lie algebras of diagonal type, Lie Algebras and Related Topics 652 (2015) 47–60.
A. A. Baranov, A. Mudrov, H. M. Shlaka, Wedderburn-Malcev decomposition of one-sided ideals of finite dimensional algebras, Communications in Algebra 46(8) (2018) 3605–3607.
A. A. Baranov, J. Rowley, Inner ideals of simple locally finite Lie algebras, Journal of Algebra 379 (2013) 11–30.
A. A. Baranov, H. Shlaka, Jordan-Lie inner ideals of finite dimensional associative algebras, Journal of Pure and Applied Algebra 224(5) (2020) 106189.
A. A. Baranov, A. G. Zhilinskii, Diagonal direct limits of simple Lie algebras, Communications in Algebra 27(6) (1999) 2749–2766.
A. Fernandez Lopez, E. Garcia, M. Gomez Lozano, Inner ideals of finitary simple Lie algebras, Journal of Lie Theory 16(1) (2006) 97–114.
H. M. Shlaka, Locally finite associative algebras and their Lie subalgebras, Journal of Physics: Conference Series, IOP Publishing 1591 (2020) 012058.
