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Department of Mathematics

Algebra Research Group

Our group is engaged in a wide variety of research topics in algebra and related fields.

In the scope of our member's interests are representation theory of algebraic groups, quantum groups, function algebras of quantum groups, quivers and related geometry; Lie theory, vertex operator algebras, canonical bases, Hall algebras; cohomology theory of finite groups; non-commutative algebraic geometry, algebraic deformation theory; algebraic topology and homotopy theory, homological methods in representation theory and homotopical method in finite group theory, local group theory, two-dimensional conformal field theory, string theory, discrete mathematics, combinatorics, finite geometry.

$$\begin{array}{ccc} {\rm Hom}(A,X) & \stackrel{\Phi_X}{\longrightarrow} & F(X) \\ {\scriptsize f\circ}\downarrow\quad & & \quad\ \downarrow {\scriptsize F(f)} \\ {\rm Hom}(A,Y) & \stackrel{\Phi_Y}{\longrightarrow} & F(Y) \\ \end{array} \qquad \longleftrightarrow \qquad \Phi_A({\rm id}_A)\in F(A) $$