Left-right symmetry of the finitistic dimension
The finitistic dimension conjecture is the assertion that the finitistic dimension of a finite dimensional algebra is finite. This dimension can be defined in terms of left or right modules. In general, the left and right finitistic dimensions of an algebra are not equal, but it is unknown if the finiteness of the two dimensions is connected. In this talk, we will translate the conjecture into a question about the connection between the left and right finitistic dimensions of an algebra using quiver operations.