Abstract
AbstractThe main goal of this chapter is a detailed construction of the free braided Hopf algebra \(\mathbf{k}\langle V \rangle\) and the shuffle braided Hopf algebra Sh τ (V ) on the tensor space of a given braided space V. Then we define a Nichols algebra \(\mathcal{B}(V )\) as a subalgebra generated by V in Sh τ (V ) and provide some characterizations of it. Finally we adopt the Radford biproduct and the Majid bozonization to character Hopf algebras. All calculations are done in the braid monoid (not in the braid group), therefore in the constructions there is no need to assume that the braiding is invertible.KeywordsHopf AlgebraCommutation RuleDrinfeld ModuleBraided Monoidal CategoryNichols AlgebraThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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