Monday, January 13 at 3:30pm to 4:30pm

This is a past event.

Kaprielian Hall (KAP), 245

3620 South Vermont Avenue, Los Angeles, CA 90089

**Taiki Shibata, Okayama University of Science**

Abstract:

An algebraic supergroup is a group-valued functor on the category of

commutative superalgebras ($=Z/2Z$-graded algebra) represented by a finitely

generated commutative Hopf superalgebra. It has been known that

representations of algebraic supergroups can be applied in non-super

(modular) representation theory. In 2011, V. Serganova introduced the notion

of quasireductive supergroups as a super-version of the notion of split

reductive groups. They form a large class of algebraic supergroups including

Chevalley supergroups (introduced by R. Fioresi and F. Gavarini, 2012) and

queer supergroups $Q(n)$ (whose Lie superalgebra is a queer superalgebra

$q(n)$). She constructed irreducible representations of quasireductive

supergroups over an algebraically closed field of characteristic zero, in

terms of their Lie superalgebras.

In this talk, I will explain a Hopf-algebraic approach to the study of

quasireductive supergroups and, as an application, I will give a

generalization of Serganova's construction to the case when the base field

is arbitrary. The main tool of the construction is a super-version of the

hyperalgebra $hy(G)$ of an algebraic group $G$ (due to M. Takeuchi) which is

a refinement of the notion of the Lie algebra $Lie(G)$ of $G$.

- Event Type
- Campus

- Department
- Mathematics
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