# Semi-simplicity of Temperley-Lieb Algebras of type D

15 Mar 2020 Li Yanbo Shi Xiaolin

We provide a necessary and sufficient condition for a type D Temperley-Lieb algebra ${\rm TLD}_n(\delta)$ being semi-simple by studying branching rule for cell modules. As a byproduct, our result is used to study the so-called forked Temperley-Lieb algebra, which is a quotient algebra of ${\rm TLD}_n(\delta)$...

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• REPRESENTATION THEORY
• RINGS AND ALGEBRAS