Christopher M. Drupieski
Representations and cohomology for Frobenius-Lusztig kernels.
Tue, 04/27/2010 - 15:01 — SomNambulAuthors: Christopher M. Drupieski
Subjects: Representation Theory
AbstractLet $U_\zeta$ be the quantum group (Lusztig form) associated to the simple
Lie algebra $\mathfrak{g}$, with parameter $\zeta$ specialized to an $\ell$-th
root of unity in a field of characteristic $p>0$. In this paper we study
certain finite-dimensional normal Hopf subalgebras $U_\zeta(G_r)$ of $U_\zeta$,
called Frobenius-Lusztig kernels, which generalize the Frobenius kernels $G_r$
of an algebraic group $G$. When $r=0$, the algebras studied here reduce to the
small quantum group introduced by Lusztig. We classify the irreducible
$U_\zeta(G_r)$-modules and discuss their characters.Injectivity criteria and support varieties for the small quantum group.
Fri, 10/16/2009 - 17:25 — SomNambulAuthors: Christopher M. Drupieski
Subjects: Representation Theory
AbstractLet $u_\zeta(g)$ denote the small quantum group associated to the simple
complex Lie algebra $g$, with parameter $q$ specialized to a primitive
$\ell$-th root of unity $\zeta$ in the field $k$. Generalizing a result of
Cline, Parshall and Scott, we show that if $M$ is a finite-dimensional
$u_\zeta(g)$-module admitting a compatible torus action, then the injectivity
of $M$ as a module for $u_\zeta(g)$ can be detected by the restriction of $M$
to certain root subalgebras of $u_\zeta(g)$.Injectivity criteria and support varieties for the small quantum group.
Fri, 10/16/2009 - 17:25 — SomNambulAuthors: Christopher M. Drupieski
Subjects: Representation Theory
AbstractLet $u_\zeta(g)$ denote the small quantum group associated to the simple
complex Lie algebra $g$, with parameter $q$ specialized to a primitive
$\ell$-th root of unity $\zeta$ in the field $k$. Generalizing a result of
Cline, Parshall and Scott, we show that if $M$ is a finite-dimensional
$u_\zeta(g)$-module admitting a compatible torus action, then the injectivity
of $M$ as a module for $u_\zeta(g)$ can be detected by the restriction of $M$
to certain root subalgebras of $u_\zeta(g)$.
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