Mapping cones of monomial ideals over exterior algebras

Let K be a field, V a finite dimensional K-vector space and E the exterior algebra of V.We analyze iterated mapping cone over E. If I is a monomial ideal of E with linear quotients, we show that the mapping cone construction yields a minimal graded free resolution F of I via the Cartan complex. Moreover, we provide an explicit description of the differentials in F when the ideal I has a regular decomposition function. Finally, we get a formula for the graded Betti numbers of a new class of monomial ideals including the class of strongly stable ideals.