Abstract
Invariant theory seeks to determine whether a (mathematical) object can be obtained from some other object by the action of some group. One way to answer this question is to find some functions that map from the class of objects to some field (or more generally some ring). Invariants are functions which take the same value on any two objects which are related by an element of the group. Thus if we can find any invariant which takes different values on two objects, then these two objects cannot be related by an element of the group. Ideally, we hope to find enough invariants to separate all objects which are not related by any group element. This means we want to find a (finite) set of invariants f 1,f 2,…,f r with the property that if two objects are not related by the group action then at least one of these r invariants takes different values on the two objects in question.
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
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Campbell, H.E.A.E., Wehlau, D.L. (2011). First Steps. In: Modular Invariant Theory. Encyclopaedia of Mathematical Sciences, vol 139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17404-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-17404-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17403-2
Online ISBN: 978-3-642-17404-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)