@article{Deng2026, 
author = {Chao Deng and Xiaomin Tang},
title = {Matrix representation of    λ  −oscillator algebras and their corresponding Leibniz algebras},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {5},
pages = {3079-3092},
keywords = {oscillator algebra, Lie algebra, matrix representation, algebra representation, Leibniz algebra},
url = {https://www.sciopen.com/article/10.3934/era.2026139},
doi = {10.3934/era.2026139},
abstract = {In this paper, we systematically characterize the types of oscillator algebras, ranging from the simplest case              D        4   to the most general              D              2      m      +      2              λ      . Subsequently, we construct multiple faithful matrix representations and vector field representations for              D              2      m      +      2              λ        (      R    ), and give a non-go theorem for a certain representation of              D              2      m      +      2              λ        (      C    ). Furthermore, leveraging the faithful representation of              D              2      m      +      2              λ        (      R    ) via the special symplectic Lie algebra              s      p              2      m      +      2        (      R    ), we establish a Leibniz algebra associated with              D              2      m      +      2              λ        (      R    ).}
}