Braidings of Tensor Spaces

Abstract

Let $V$ be a braided vector space, that is, a vector space together with a solution $\hat{R}\in \text{End}(V\otimes V)$ of the Yang--Baxter equation. Denote $T(V):={⨁}_k{V}^{\otimes k}$. We associate to $\hat{R}$ a solution $T(\hat{R})\in \text{End}(T(V)\otimes T(V))$ of the Yang--Baxter equation on the tensor space $T(V)$. The correspondence $\hat{R}⇝T(\hat{R})$ is functorial with respect to $V$.

10 pages, no figures

References in corpus (3)

• Orthogonal and Symplectic Quantum Matrix Algebras and Cayley-Hamilton Theorem for them
• Braids, Shuffles and Symmetrizers
• Braidings of Tensor Spaces

Cited by in corpus (3)

• Braids, Shuffles and Symmetrizers
• Braidings of Tensor Spaces
• Cyclotomic shuffles