Various subgroups of Aut(Cn)${\rm{Aut}}({\mathbb{C}}^{n})$. Issue 3 (26th December 2022)

• Record Type: Journal Article
• Authors: Lin, Zhangli; Zhou, Xiangyu
• Is Part Of: Proceedings of the London Mathematical Society. Volume 126:Issue 3(2023)
• Page Start: 880
• Page End: 899
• Publication Date: 2022-12-26
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1112/plms.12501
• Languages: English
• ISSNs: 0024-6115

Abstract

Abstract: In this paper, using ideas of Andersén and Lempert on the group of holomorphic automorphisms Aut ( C n ) ${\rm{Aut}}({\mathbb{C}}^{n})$ ( n ⩾ 2 $n\geqslant 2$ ), we prove that the subgroups in Aut ( C n ) ${\rm{Aut}}({\mathbb{C}}^{n})$ and Aut sp ( C 2 n ) ${\rm{Aut}}_{\rm{sp}}({\mathbb{C}}^{2n})$ ( n ⩾ 2 $n\geqslant 2$ ) generated by different types of 'shears' are all distinct, which answer affirmatively to two conjectures posed by Forstnerič.