We determine six invariant subspaces of the 16-dimensional space gl_4(R) under the conjugation by any element in Spin_3(R). Four of them add up to the 10-dimensional space of symmetric matrices and the other two add up to the 6-dimensional space of skew-symmetric matrices.
Falcone, G. (2010). A spinorial decomposition of gl_4(R). In T. Brugarino, M.S. Mongiovì (a cura di), Bollettino di Matematica pura e applicata III (pp. 71-78). Roma : Aracne.
A spinorial decomposition of gl_4(R)
FALCONE, Giovanni
2010-01-01
Abstract
We determine six invariant subspaces of the 16-dimensional space gl_4(R) under the conjugation by any element in Spin_3(R). Four of them add up to the 10-dimensional space of symmetric matrices and the other two add up to the 6-dimensional space of skew-symmetric matrices.
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