Abstract
Let E be a vector space and G be an abelian group. Suppose that a direct decomposition
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
.
In this chapter all vector spaces are defined over a fixed, but arbitrarily chosen field τ of characteristic 0.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1975 Springer-Verlag New York Inc.
About this chapter
Cite this chapter
Greub, W. (1975). Gradations and homology. In: Linear Algebra. Graduate Texts in Mathematics, vol 23. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9446-4_7
Download citation
DOI: https://doi.org/10.1007/978-1-4684-9446-4_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4684-9448-8
Online ISBN: 978-1-4684-9446-4
eBook Packages: Springer Book Archive