permutation operator
Let be a vector space over a field. Let , the symmetric group on and define a multilinear map by
Then by the universal factorization property (http://planetmath.org/TensorProduct) for a tensor product (http://planetmath.org/TensorProduct) there is a unique linear map such that . Then of course,
is called the permutation operator associated with .
1 Properties
-
1.
-
2.
, where is the identity mapping on
-
3.
is nonsingular and
Title | permutation operator |
---|---|
Canonical name | PermutationOperator |
Date of creation | 2013-03-22 16:15:38 |
Last modified on | 2013-03-22 16:15:38 |
Owner | Mathprof (13753) |
Last modified by | Mathprof (13753) |
Numerical id | 7 |
Author | Mathprof (13753) |
Entry type | Definition |
Classification | msc 15A04 |