Theoretical Statistics and Mathematics Unit, ISI Delhi

August 14, 2013 (Wednesday) ,
3:30 PM at Webinar

Speaker:
Neha Hooda,
Indian Statistical Institute, Delhi

Title:
Mod-2 Invariants of Algebraic Groups $G_2$ and $F_4$

Abstract of Talk

Let $k$ be a field of characteristic different from $2$ and
$3$. Let $G$ be a simple algebraic group of type $G_2$ or $F_4$ over
$k$. It is known that groups of type $G_2$ over $k$ occur as groups of
automorphisms of octonion algebras and groups of type $F_4$ over $k$
are precisely the groups of automorphisms of Albert algebras. These
algebras define certain mod-2 (Galois cohomological) invariants of
these groups. In this talk we will discuss how these invariants
determine $k$-embeddings of groups of type $A_1$ and $A_2$ in $G$.
Moreover, $k$-groups of type $F_4$ (resp. $G_2$) are generated by
$k$-subgroups of type $A_2$ (resp. $A_1$). This motivates the study of
embeddings mentioned above.