Linear Algebra pp 167-185 | Cite as

Gradations and homology

  • Werner Greub
Part of the Graduate Texts in Mathematics book series (GTM, volume 23)


Let E be a vector space and G be an abelian group. Suppose that a direct decomposition
$$E = \sum\nolimits_{\alpha \in I} {{E_\alpha }} $$
is given and that to every subspace E α an element k(α) of G is assigned such that the mapping a→k((x) is injective. Then E is called a G-graded vector space. G is called the group of degrees for E. The vectors of E α are called homogeneous of degree k (α) and we shall write
$$\deg x = k(\alpha ),x \in {E_\alpha }$$


Degree Zero Homogeneous Element Linear Isomorphism Differential Algebra Grade Vector Space 
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Copyright information

© Springer-Verlag New York Inc. 1975

Authors and Affiliations

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

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