Koszulity for nonquadratic algebras II

Details Koszulity for nonquadratic algebras II Koszulity for nonquadratic algebras II

2003-01-16

arxiv.org/abs/math/0301172v1

Mathematics

Quantum Algebra

Corrigendum to Koszulity for nonquadratic algebras. J. Algebra 239, No.2, 705-734 (2001); 2 pages

Scientific paper

It has been shown recently, in a joint work with Michel Dubois-Violette and Marc Wambst (see math.QA/0203035), that Koszul property of $N$-homogeneous algebras (as defined in the original paper) becomes natural in a $N$-complex setting. A basic question is to define the differential of the bimodule Koszul complex of an $N$-homogeneous algebra, e.g., for computing its Hochschild homology. The differential defined here uses $N$-complexes. That puts right the wrong differential presented in the original paper in a 2-complex setting. Actually, as we shall see, it is impossible to avoid $N$-complexes in defining the differential, whereas the bimodule Koszul complex is a 2-complex.

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