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A braided vector space is a pair $(V,\sigma)$ consisting of a vector space $V$, and a linear map $\sigma:V \otimes V \to V \otimes V$, satisfying the Yang--Baxter equation. Ee can scale the braiding ...

Given a Hopf algebra $H$ and a Yetter--Drinfeld module $V$ over $H$, it is well-known that $V$ has an induced braided vector space structure, and so, one can consider it's Nichols algebra which is a ...

Many important concepts in tensor category theory have their counterpart in Hopf algebra theory under Tannaka duality. They have the general form: let $A$ be an XX-algebra, and let Rep$(A)$ denote the ...

In Chapter XVI Kassel introduces a proper definition of a quantum universal enveloping algebra of a Lie algebra $\mathfrak{g}$. (See definition XVI.5.1). Notice that a quantum enveloping algebra has a ...