The Fine Moduli Space of Representations of Clifford Algebras

Details The Fine Moduli Space of Representations of Clifford Algebras The Fine Moduli Space of Representations of Clifford Algebras

2009-11-15

arxiv.org/abs/0911.2894v3

Mathematics

Rings and Algebras

Final version. To appear in Int. Math. Res. Not. IMRN

Scientific paper

Given a fixed binary form $f(u,v)$ of degree $d$ over a field $k$, the associated \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 $(\alpha u+\beta v)^{d}-f(\alpha,\beta)$ with $\alpha$ and $\beta$ arbitrary elements in $k$. All representations of $C_f$ have dimensions that are multiples of $d$, and occur 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 $r \geq 2$. Our construction starts with the projective curve $C \subset \mathbb{P}^{2}_{k}$ defined by the equation $w^d=f(u,v)$, 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 $d_r=r(d+g-1)$, where $g$ denotes the genus of $C$.

Affiliated with

Also associated with

No associations

Rating

The Fine Moduli Space of Representations of Clifford Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Fine Moduli Space of Representations of Clifford Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Fine Moduli Space of Representations of Clifford Algebras will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-324131