A diagrammatic categorification of the fermion algebra

In this paper, we study the diagrammatic categorification of the fermion algebra. We construct a graphical category corresponding to the one-dimensional （1D） fermion algebra, and we investigate the properties of this category. The categorical analogues of the Fock states are some kind of 1-morphisms in our category, and the dimension of the vector space of 2-morphisms is exactly the inner product of the corresponding Fock states. All the results in our categorical framework coincide exnetlv with those in normal quantum mechanics.     

Descent Equations Starting from High Rank Chern-Simons

In this paper a set of generalized descent equations are proposed. The solutions to those descent equations labeled by r for any r(r ≥ 2, r ∈ N) are forms of degrees varying from 0 to(2r-1). And the case of r = 2 is mainly discussed.