컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0557 |
|---|---|
| 분류(Section) | Poster Session |
| 분과(Session) | Algebra / Representation Theory / Lie Theory (SS-02) |
| 영문제목 (Title(Eng.)) |
[CANCELLED] On the embedding $Sp(2)\stackrel{\varphi}{\rightarrow} O(4)$ |
| 저자(Author(s)) |
Clarisson Rizzie Canlubo1 Mathematics Society of the Philippines1 |
| 초록본문(Abstract) | It is well known in Lie theory that $Sp(n)$ canonically embeds as a Lie subgroup of $O(4n)$. In particular, $Sp(2)$ embeds in $O(8)$ but no known embedding $Sp(2)\hookrightarrow O(4)$. In this paper, we express orthogonal transformations of $\mathbb{R}^{4}$ as M$\ddot{o}$bius transformations involving quaternion matrices. This incidentally gives a way of embedding $Sp(2)\stackrel{\varphi}{\rightarrow}O(4)$ that factors through the stereographic projection $\mathcal{S}^{3}\stackrel{\pi}{\rightarrow}\mathbb{H}^{*}$ where $\mathbb{H}^{*}$ is the subspace of pure imaginary quaternions. We will also describe the spectral geometry of $2\times 2$ quaternion matrices using $\varphi$. |
| 분류기호 (MSC number(s)) |
51B10, 15B33 |
| 키워드(Keyword(s)) | Mobius transformations, quaternions |
| 강연 형태 (Language of Session (Talk)) |
English |