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  Braid rigidity for path algebras

Martirosyan, L., & Wenzl, H. (in press). Braid rigidity for path algebras. Indiana University Mathematics Journal, To appear.

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2001.11440.pdf (Preprint), 240KB
 
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 Creators:
Martirosyan, Lilit1, Author           
Wenzl, Hans, Author
Affiliations:
1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Quantum Algebra, Category Theory, Representation Theory
 Abstract: Path algebras are a convenient way of describing decompositions of tensor
powers of an object in a tensor category. If the category is braided, one
obtains representations of the braid groups $B_n$ for all $n\in \N$. We say
that such representations are rigid if they are determined by the path algebra
and the representations of $B_2$. We show that besides the known classical
cases also the braid representations for the path algebra for the 7-dimensional
representation of $G_2$ satisfies the rigidity condition, provided $B_3$
generates $\End(V^{\otimes 3})$. We obtain a complete classification of ribbon
tensor categories with the fusion rules of $\g(G_2)$ if this condition is
satisfied.

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Language(s): eng - English
 Dates: 2020
 Publication Status: Accepted / In Press
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: arXiv: 2001.11440
 Degree: -

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Title: Indiana University Mathematics Journal
Source Genre: Journal
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Publ. Info: Indiana University
Pages: - Volume / Issue: - Sequence Number: To appear Start / End Page: - Identifier: -