Frontiers of Mathematics in China >

2023 , Vol. 18 >Issue 5: 353 - 365

DOI: https://doi.org/10.3868/s140-DDD-023-0025-x

Infinite-dimensional necklace Lie algebras and some finite-dimensional important subalgebras

  • Demin YU , 1 ,
  • Caihui LU 2
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  • 1. College of Mathematics, Hunan Institute of Science and Technology, Yueyang 414000, China
  • 2. School of Mathematical Sciences, Capital Normal University, Beijing 100037, China
yudeming8640024@126.com

Published date: 15 Oct 2023

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2023 Higher Education Press 2023
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Abstract

In this paper, a new infinite-dimensional necklace Lie algebra is studied and the left and right index arrays of a necklace word in necklace Lie algebra is first defined. Using the left and right index arrays, we divide the necklace words into 5 classes. We discuss finite-dimensional Lie subalgebras of necklace Lie algebras intensively and prove that some subalgebras are isomorphism to simple Lie algebra sl(n).

Key words： Necklace Lie algebra; left and right index arrays; subalgebra

Cite this article

Demin YU , Caihui LU . Infinite-dimensional necklace Lie algebras and some finite-dimensional important subalgebras[J]. Frontiers of Mathematics in China, 2023 , 18(5) : 353 -365 . DOI: 10.3868/s140-DDD-023-0025-x

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