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

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\left(n\right).

Graphical abstract

Keywords

Necklace Lie algebra / left and right index arrays / subalgebra

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