The Fine Moduli Space of Representations of Clifford Algebras - Mathematics > Rings and Algebras

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Abstract: Given a fixed binary form $fu,v$ of degree $d$ over a field $k$, theassociated \emph{Clifford algebra} is the $k$-algebra $C f=k\{u,v\}-I$, where$I$ is the two-sided ideal generated by elements of the form $\alpha u+\betav^{d}-f\alpha,\beta$ with $\alpha$ and $\beta$ arbitrary elements in $k$.All representations of $C f$ have dimensions that are multiples of $d$, andoccur in families. In this article we construct fine moduli spaces $U=U {f,r}$for the irreducible $rd$-dimensional representations of $C f$ for each $r \geq2$. Our construction starts with the projective curve $C \subset\mathbb{P}^{2} {k}$ defined by the equation $w^d=fu,v$, and produces$U {f,r}$ as a quasiprojective variety in the moduli space $\mathcal{M}r,d r$of stable vector bundles over $C$ with rank $r$ and degree $d r=rd+g-1$,where $g$ denotes the genus of $C$.

Autor: Emre Coskun

Fuente: https://arxiv.org/