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- W2898077206 abstract "Let $mathcal{C}$ be a decomposable plane curve over an algebraically closed field $k$ of characteristic 0. That is, $mathcal{C}$ is defined in $k^2$ by an equation of the form $g(x) = f(y)$, where $g$ and $f$ are polynomials of degree at least 2. We use this data to construct 3 pointed Hopf algebras, $A(x,a,g)$, $A(y,b,f)$ and $A(g,f)$, in the first two of which $g$ [resp. $f$] are skew primitive central elements, and the third being a factor of the tensor product of the first two. We conjecture that $A(g,f)$ contains the coordinate ring $mathcal{O}(mathcal{C})$ of $mathcal{C}$ as a quantum homogeneous space, and prove this when each of $g$ and $f$ has degree at most 5 or is a power of the variable. We obtain many properties of these Hopf algebras, and show that, for small degrees, they are related to previously known algebras. For example, when $g$ has degree 3 $A(x,a,g)$ is a PBW deformation of the localisation at powers of a generator of the downup algebra $A(-1,-1,0)$." @default.
- W2898077206 created "2018-10-26" @default.
- W2898077206 creator A5025628466 @default.
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- W2898077206 date "2018-10-22" @default.
- W2898077206 modified "2023-09-27" @default.
- W2898077206 title "Plane curves which are quantum homogeneous spaces" @default.
- W2898077206 doi "https://doi.org/10.48550/arxiv.1810.09509" @default.
- W2898077206 hasPublicationYear "2018" @default.
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