Abstract
After presenting the exterior algebra in Sect. 2.1, the remaining three sections are devoted to the main aspects of this algebra that depend on the metric, namely the contraction operator, Sect. 2.2, the extension of the metric to the whole algebra, Sect. 2.3, and the inner product, Sect. 2.4. The point of view here is to call Grassmann algebra to the structure formed by the exterior algebra enriched with the metric, the inner product, and the parity and reverse involutions.
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References
H.G. Grassmann, Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik (Otto Wiegand, Leipzig, 1844)
H.G. Grassmann, Die Ausdehnungslehre. Vollständig und in strenger Form (Adolf Enslin, Berlin, 1862)
H.G. Grassmann, Extension Theory (American Mathematical Society, Providence, 2000). Translated from the German version Die Ausdehnungslehre von 1862 by Lloys C. Kannenberg
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Xambó-Descamps, S. (2018). Grassmann Algebra. In: Real Spinorial Groups. SpringerBriefs in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-00404-0_2
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DOI: https://doi.org/10.1007/978-3-030-00404-0_2
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