| Title:
|
Spin representations and binary numbers (English) |
| Author:
|
Winther, Henrik |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
60 |
| Issue:
|
4 |
| Year:
|
2024 |
| Pages:
|
231-241 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider a construction of the fundamental spin representations of the simple Lie algebras $\mathfrak{so}(n)$ in terms of binary arithmetic of fixed width integers. This gives the spin matrices as a Lie subalgebra of a $\mathbb{Z}$-graded associative algebra (rather than the usual $\mathbb{N}$-filtered Clifford algebra). Our description gives a quick way to write down the spin matrices, and gives a way to encode some extra structure, such as the real structure which is invariant under the compact real form, for some $n$. Additionally we can encode the spin representations combinatorially as (coloured) graphs. (English) |
| Keyword:
|
spin group |
| Keyword:
|
fundamental representations |
| Keyword:
|
spin matrices |
| Keyword:
|
binary numbers |
| MSC:
|
22E46 |
| DOI:
|
10.5817/AM2024-4-231 |
| . |
| Date available:
|
2024-11-27T08:34:52Z |
| Last updated:
|
2024-11-27 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152642 |
| . |
| Reference:
|
[1] Baum, H., Friedrich, Th., Grunewald, R., Kath, I.: Twistors and Killing spinors on Riemannian manifolds.Teubner Verlag Leipzig, Stuttgart, 1991. Zbl 0734.53003, MR 1164864 |
| . |
