The homological shift algebra of a monomial ideal

Official URL: https://dx.doi.org/10.1007/s13348-026-00513-2

Let be the polynomial ring over a field K, and let be a monomial ideal. In this paper, we introduce the i-th homological shift algebras of I. When I has linear powers, these K-algebras have the structure of a finitely generated bigraded module over the Rees algebra of I. Hence, many invariants of, such as depth, associated primes, regularity, and the -number, exhibit well behaved asymptotic behavior. We determine several families of monomial ideals I for which has linear resolution for all. Finally, we show that is Golod for all monomial ideals with linear powers and all.