K-projectors

We study representations of a free associative algebra \(T^*(W\otimes W^*)\) in a vector space \(V\) with the property \(V\otimes V\cong V\oplus V_0\) where \(T^*(W\otimes W^*)\) acts by zero on \(V_0\) and the tensor product \(V\otimes V\) of representations corresponds to the natural homomorphism...

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Bibliographic Details
Published in:arXiv.org 2017-07
Main Author: Odesskii, Alexander
Format: Article
Language:English
Subjects:
Homomorphisms
Projectors
Representations
Tensors
Online Access:Get full text
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Summary:We study representations of a free associative algebra \(T^*(W\otimes W^*)\) in a vector space \(V\) with the property \(V\otimes V\cong V\oplus V_0\) where \(T^*(W\otimes W^*)\) acts by zero on \(V_0\) and the tensor product \(V\otimes V\) of representations corresponds to the natural homomorphism \(W\otimes W^*\to W\otimes W^* \otimes W\otimes W^*\). We develop an algebraic theory of such objects and construct a lot of examples.
ISSN:2331-8422