On the non-existence of left-invariant hypercomplex structures on $SU(2)^{4n}$
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918135496441856 |
|---|---|
| author | Pham, David N. |
| author_facet | Pham, David N. |
| contents | Using elementary algebraic arguments, it is shown that $SU(2)^{m}:=SU(2)\times \cdots \times SU(2)$ ($m$ times) admits no left-invariant hypercomplex structures for all $m\ge 1$. This result answers (in a clear and easily accessible way) the question of whether every compact Lie group of dimension $4n$ admits a left-invariant hypercomplex structure. The aforementioned question has apparently been the source of some confusion in the recent literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_21766 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the non-existence of left-invariant hypercomplex structures on $SU(2)^{4n}$ Pham, David N. Differential Geometry 53C15, 53C26, 32Q60 Using elementary algebraic arguments, it is shown that $SU(2)^{m}:=SU(2)\times \cdots \times SU(2)$ ($m$ times) admits no left-invariant hypercomplex structures for all $m\ge 1$. This result answers (in a clear and easily accessible way) the question of whether every compact Lie group of dimension $4n$ admits a left-invariant hypercomplex structure. The aforementioned question has apparently been the source of some confusion in the recent literature. |
| title | On the non-existence of left-invariant hypercomplex structures on $SU(2)^{4n}$ |
| topic | Differential Geometry 53C15, 53C26, 32Q60 |
| url | https://arxiv.org/abs/2505.21766 |