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Finite-dimensional special contact superalgebras of odd type over a field of prime characteristic

Volume 155 / 2019

Jixia Yuan, Wende Liu, Yan Cao Colloquium Mathematicum 155 (2019), 255-266 MSC: Primary 17B50; Secondary 17B70. DOI: 10.4064/cm7415-3-2018 Published online: 7 December 2018


We consider an infinite family of finite-dimensional Lie superalgebras over a field $\mathbb{F}$ of characteristic $p \gt 2$, special contact Lie superalgebras of odd type, denoted by $\mathfrak{sm}_{\lambda}(n;\underline{N})$ and parameterized by $\lambda\in \mathbb{F}$. The second derived subalgebra of $\mathfrak{sm}_{\lambda}(n;\underline{N})$ is proved to be simple by finding a linear spanning set of $\mathfrak{sm}_{\lambda}(n;\underline{N})$. In the process a direct sum decomposition of $\mathfrak{sm}_{\lambda}(n;\underline{N})$ is given in terms of its first or second derived subalgebras. Moreover, dimension formulas for these Lie superalgebras are established and comparison with the known simple Lie superalgebras of Cartan type shows that the second derived subalgebras of the Lie superalgebras $\mathfrak{sm}_{\lambda}(n;\underline{N})$ constitute a new infinite family of finite-dimensional simple Lie superalgebras.


  • Jixia YuanSchool of Mathematical Sciences
    Heilongjiang University
    150080 Harbin, China
  • Wende LiuSchool of Mathematics and Statistics
    Hainan Normal University
    571158 Haikou, China
  • Yan CaoCollege of Rongcheng
    Harbin University of Science and Technology
    264300 Rongcheng, China

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