We study holonomy algebras generated by an algebraic element of the Clifford algebra, or equivalently, the holonomy algebras of certain spin connections in flat space. We provide series of examples in arbitrary dimensions and establish general properties of the holonomy algebras under some mild conditions on the generating element.
1
Dept. of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand
Niels Bernhardt; Paul-Andi Nagy. On Algebraic Torsion Forms and their Spin Holonomy Algebras. Journal of Lie Theory, Tome 17 (2007) no. 2, pp. 357-377. http://geodesic.mathdoc.fr/item/JOLT_2007_17_2_a7/
@article{JOLT_2007_17_2_a7,
author = {Niels Bernhardt and Paul-Andi Nagy},
title = {On {Algebraic} {Torsion} {Forms} and their {Spin} {Holonomy} {Algebras}},
journal = {Journal of Lie Theory},
pages = {357--377},
year = {2007},
volume = {17},
number = {2},
url = {http://geodesic.mathdoc.fr/item/JOLT_2007_17_2_a7/}
}
TY - JOUR
AU - Niels Bernhardt
AU - Paul-Andi Nagy
TI - On Algebraic Torsion Forms and their Spin Holonomy Algebras
JO - Journal of Lie Theory
PY - 2007
SP - 357
EP - 377
VL - 17
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2007_17_2_a7/
ID - JOLT_2007_17_2_a7
ER -
%0 Journal Article
%A Niels Bernhardt
%A Paul-Andi Nagy
%T On Algebraic Torsion Forms and their Spin Holonomy Algebras
%J Journal of Lie Theory
%D 2007
%P 357-377
%V 17
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2007_17_2_a7/
%F JOLT_2007_17_2_a7
