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We study the algebraic structure of the Dirac fermion state in the organicconductor, \alpha-(BDET-TTF)_2I_3. We find a pair of generators for theHamiltonian of \alpha-(BDET-TTF)_2I_3 that describes the chirality of Diracfermions. The phase parameters associated with those generators have anintimate and simple relationship with the positions of the Dirac points in theBrillouin zone. By making use of the form of the generators, a reduced form ofthe Hamiltonian is constructed that shares some characteristic features of theDirac fermions with \alpha-(BDET-TTF)_2I_3. For the reduced Hamiltonian wepresent the analytic expression for the Dirac point position that sits atarbitrary point in the Brillouin zone determined by the hopping parameters.

Algebraic structure of Dirac fermion state in \alpha-(BDET-TTF)_2I_3