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

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

2008-12-17

arxiv.org/abs/0812.3408v2

Mathematics

Representation Theory

Scientific paper

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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