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Lie Z-graded Algebraic Formalism for Observer Fields
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2004 International Mathematica Symposium
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Banff, Canada
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The aim of this paper is to present a symbolic calculation approach for the basic facts for the Lie a-graded (super) algebra of derivations of the Grassmann algebra of differential forms, the -graded Gerstenhaber algebras, the Frölicher-Nijenhuis algebra of vector-valued differential multi-forms, and the Schouten-Nijenhuis algebra of multi-vector fields. These algebras are the necessary algebraic formalism in order to understand an accelerated observer field (a 3+1 split), as an almost product structure (1,1)-tensor field acting on the Grassmann algebras as the derivation.
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Lie Z-graded Algebraic Formalism, Observer Fields, algebra of derivations, Grassmann algebra of differential forms, Gerstenhaber algebras, Froelicher-Nijenhuis algebra, algebraic formalism, accelerated observer field
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