Let \((g,~[-,-],~\omega )\) be a finite-dimensional complex \(\omega \)-Lie superalgebra. In this paper, we introduce the notions of derivation superalgebra \({\mathrm{Der}}(g)\) and the automorphism group \({\mathrm{Aut}}(g)\) of \((g,~[-,-],~\omega )\). We study \({\mathrm{Der}}^{\omega }(g)\) and \({\mathrm{Aut}}^{\omega }(g)\), which are superalgebra of \({\mathrm{Der}}(g)\) and subgroup of \({\mathrm{Aut}}(g)\), respectively. For any 3-dimensional or 4-dimensional complex \(\omega \)-Lie superalgebra g, we explicitly calculate \({\mathrm{Der}}(g)\) and \({\mathrm{Aut}}(g)\), and obtain Jordan standard forms of elements in the two sets. We also study representation theory of \(\omega \)-Lie superalgebras and give a conclusion that all nontrivial non-\(\omega \)-Lie 3-dimensional and 4-dimensional \(\omega \)-Lie superalgebras are multiplicative, as well as we show that any irreducible respresentation of the 4-dimensional \(\omega \)-Lie superalgebra \(P_{2,k}(k\ne 0,-1)\) is 1-dimensional.

设\(((g,~[-,-],~\omega )\)是一个有限维复数\(\omega \) -李超代数。在本文中，我们介绍推导代数的概念\（{\ mathrm {明镜}}（G）\）和自同构组\（{\ mathrm {AUT}}（G）\）的\（（克，〜 [-,-],~\omega )\)。我们研究了\({\mathrm{Der}}^{\omega }(g)\)和\({\mathrm{Aut}}^{\omega }(g)\)，它们是\({\ mathrm{Der}}(g)\)和\({\mathrm{Aut}}(g)\) 的子群，分别。对于任何 3 维或 4 维复数\(\omega \) -李超代数g，我们明确计算\({\mathrm{Der}}(g)\)和\({\mathrm{Aut}}(g)\)，得到两个集合中元素的 Jordan 标准形式。我们还研究了\(\omega \) -Lie 超代数的表示理论，并得出结论：所有非平凡的非\(\omega \) -Lie 3 维和 4 维\(\omega \) -Lie 超代数都是可乘的，以及我们证明 4 维\(\omega \) -李超代数\(P_{2,k}(k\ne 0,-1)\) 的任何不可约表示都是一维的。