Stability theorem for \(\mathbb{Z}_2^n\)-Lie supergroups (Q6611840)

Existence of a unique unitary representation as an extension of a pre-representation is called the stability theorem. \textit{S. Merigon} et al. [Pac. J. Math. 257, No. 2, 431--469 (2012; Zbl 1294.22017)] have proven that the stability theorem holds in a Banach-Lie group setting. \textit{K.-H. Neeb} and \textit{H. Salmasian} [Math. Z. 275, No. 1--2, 419--451 (2013; Zbl 1277.22020)] stated that the stability theorem holds for each Lie supergroup. In this paper, the authors show that every pre-representation of a \(\mathbb Z_2^n\)- Lie supergroup has a unique extension to a unitary representation of \((G_0,\mathfrak g_\mathbb C)\).\N\NFor the entire collection see [Zbl 1544.53003].