TL;DR
This paper investigates the mathematical properties of certain maps on the exterior algebra of finite-dimensional vector spaces, establishing general results and linking them to the Palatini-Cartan formulation of General Relativity.
Contribution
It provides a comprehensive analysis of injectivity and surjectivity of these maps in full generality, applicable to any dimension and subspace, and connects these findings to a key formulation of gravity.
Findings
Proves properties of maps on exterior algebra for all dimensions
Establishes conditions for injectivity and surjectivity in general cases
Links mathematical properties to the Palatini-Cartan formulation of GR
Abstract
We consider injectivity and surjectivity of some maps on the exterior algebra of isomorphic finite-dimensional vector spaces. We prove the properties of the maps in full generality, for any dimension of the vector space and any subspace. We also draw a connection with the Palatini-Cartan formulation of General Relativity, for which these maps are of crucial importance.
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Taxonomy
TopicsGraph theory and applications