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Abstract: Associated to each subset $J$ of the nodes $I$ of a Dynkin diagram is atriangular decomposition of the corresponding Lie algebra $\mathfrak{g}$ intothree subalgebras $\widetilde{\mathfrak{g} {J}}$ generated by $e {j}$, $f {j}$for $j\in J$ and $h {i}$ for $i\in I$, $\mathfrak{n}^{-} {D}$ generated by$f {d}$, $d\in D=I\setminus J$ and its dual $\mathfrak{n} {D}^{+}$.We demonstrate a quantum counterpart, generalising work of Majid and Rosso,by exhibiting analogous triangular decompositions of $U {q}\mathfrak{g}$ andidentifying a graded braided Hopf algebra that quantizes$\mathfrak{n} {D}^{-}$. This algebra has many similar properties to$U {q}^{-}\mathfrak{g}$, in many cases being a Nichols algebra and thereforecompletely determined by its associated braiding.



Autor: Jan E. Grabowski

Fuente: https://arxiv.org/



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