d-Koszul algebras, 2-d determined algebras and 2-d-Koszul algebras

2008/12/17 by Edward L. Green, Green, Edward L., Eduardo N. Marcos +1 · 1 citation
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0812.3408

openalex publication_date 2008/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The relationship between an algebra and its associated monomial algebra is investigated when at least one of the algebras is d-Koszul. It is shown that an algebra which has a reduced \grb basis that is composed of homogeneous elements of degree d is d-Koszul if and only if its associated monomial algebra is d-Koszul. The class of 2-d-determined algebras and the class 2-d-Koszul algebras are introduced. In particular, it shown that 2-d-determined monomial algebras are 2-d-Koszul algebras and the structure of the ideal of relations of such an algebra is completely determined.

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