Jin Yun Guo
Coverings and Truncations of Graded Selfinjective Algebras.
Mon, 03/01/2010 - 16:01 — SomNambulAuthors: Jin Yun Guo
Subjects: Rings and Algebras
AbstractIn this paper, we study certain algebras related to a graded selfinjective
algebra with Nakayama translation $\tau$. We prove that a graded selfinjective
algebra is a regular covering of its orbit algebra, as a consequence, the McKay
quiver of a finite subgroup of a general linear group is a covering of the
McKay quiver of its intersection with the special linear group. We describe the
bound quiver of its Beilinson algebra.On McKay Quiver and Covering Spaces.
Wed, 02/10/2010 - 16:01 — SomNambulAuthors: Jin Yun Guo
Subjects: Representation Theory
AbstractIn this paper, we study the relationship between the McKay quivers of a
finite subgroups $G$ of special linear groups general linear groups, via some
natural extension and embedding. We show that the McKay quiver of certain
extension of a finite subgroup $G$ of $\mathrm{SL}(m,\mathbb C)$ in
$\mathrm{GL}(m,\mathbb C)$ is a regular covering of the McKay quiver of $G$,
and when embedding $G$ in a canonical way into $\mathrm{GL}(m-1,\mathbb C)$,
the new McKay quiver is obtained by adding an arrow from the Nakayama
translation of $i$ back to $i$ for each $i$.
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