My research interests are in the area of supermathematics.
In general, the structures of algebraic groups G are complicated. However, it is known that the “tangent space” Lie(G) of G which naturally forms a Lie algebra strongly reflects many properties of G. In positive characteristic, one should use the hyperalgebra hy(G) of G which is a refinemt of the notion of Lie(G) and forms a Hopf algebra.
As a super-analogue of algebraic groups (resp. Lie algebrs), algebraic supergroups (resp. Lie superalgebras) play an imprtant role not only in theoretical physics but also in mathematics. I proved that the above phenomena holds in super-world. Moreover, I showed that a Hopf algebraic approach is effective to study representations of algebraic supergroups. I would like to apply the results to study modular representations of algebraic supergroups and contribute to non-supermathematics.