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Mixed Exterior Algebra

  • Werner Greub
Part of the Universitext book series (UTX)

Abstract

A skew-symmetric map of type (p, q) from E*, E into a vector space H is a (p + q)-linear mapping
$$\psi :\underbrace {E* \times \ldots \times E*}_p \times \underbrace {E \times \ldots \times E}_q \to H$$
which satisfies
$$\psi (x_{\sigma (1)}^*, \ldots ,x_{\sigma (p)}^*;{x_{\tau (q)}}) = {\varepsilon _\sigma }{\varepsilon _\tau }\psi (x_1^*, \ldots ,x_p^*;{x_1}, \ldots ,{x_q})$$
for all permutations σ ∊ S p and ? ∊ S q .

Keywords

Basis Vector Linear Transformation Bilinear Function Composition Product Linear Isomorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1978

Authors and Affiliations

  • Werner Greub
    • 1
  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada

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