Mapping cones of monomial ideals over exterior algebras

Abstract

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.

KEYWORDS:

• Exterior algebra
• free resolutions
• mapping cones
• monomial ideals

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 13D02
• 13C13
• 15A75

Acknowledgments

We thank the anonymous referee for his/her careful reading and helpful suggestions.