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Structure and Representations of a Diagrammatic Non-Commutative Tangloid Algebra
We introduce the \emph{tangloid algebra} $\mathcal{T}_n$, a diagrammatic algebra arising from the extended tangloid category $\Ti$, and its subalgebra, the \emph{braidoid algebra} $\mathcal{B}_n$. The construction begins with the unoriented tangloid category $UTC$, inspired by Turaev's theory of kno
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