differential geometry w notes from teacher_Part_28

differential geometry w notes from teacher_Part_28 -...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 3 Di ff erential Forms 3.1 Exterior Algebra 3.1.1 Permutation Group • A group is a set G with an associative binary operation, · : G × G → G with identity, called the multiplication , such that each element has an inverse. That is, the following conditions are satisfied 1. for any three elements g , h , k ∈ G , the associativity law holds: ( gh ) k = g ( hk ); 2. there exists an identity element e ∈ G such that for any g ∈ G , ge = eg = g ; 3. each element g ∈ G has an inverse g- 1 , such that g g- 1 = g- 1 g = e • Let X be a set. A transformation of the set X is a bijective map g : X → X . • The set of all transformations of a set X forms a group Aut( X ), with com- position of maps as group multiplication. • Any subgroup of Aut( X ) is a transformation group of the set X . • The transformations of a finite set X are called permutations . • The group S p of permutations of the set Z n = { 1 , . . . , p } is called the sym- metric group of order p ....
View Full Document

{[ snackBarMessage ]}

Page1 / 2

differential geometry w notes from teacher_Part_28 -...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online