Spin representations and binary numbers

Winther, Henrik. "Spin representations and binary numbers." Archivum Mathematicum 060.4 (2024): 231-241. <http://eudml.org/doc/299379>.

@article{Winther2024,
abstract = {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.},
author = {Winther, Henrik},
journal = {Archivum Mathematicum},
keywords = {spin group; fundamental representations; spin matrices; binary numbers},
language = {eng},
number = {4},
pages = {231-241},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Spin representations and binary numbers},
url = {http://eudml.org/doc/299379},
volume = {060},
year = {2024},
}

TY - JOUR
AU - Winther, Henrik
TI - Spin representations and binary numbers
JO - Archivum Mathematicum
PY - 2024
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 060
IS - 4
SP - 231
EP - 241
AB - 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.
LA - eng
KW - spin group; fundamental representations; spin matrices; binary numbers
UR - http://eudml.org/doc/299379
ER -