by Berger, Roland

Any quadratic algebra endowed with an ordered set of generators can bedescribed by some linear map called a reduction operator. The general lineargroup naturally acts on reduction operators, which allows us to introduceweak and strong confluence. With respect to these notions, a completeclassification for two generators and complex coefficients is obtainedshowing that weak confluence is equivalent to Koszulity in this case. Bycontrast, some Sklyanin algebras with three generators fail to be weaklyconfluent. For an arbitrary number of generators and under some assumptionson the first terms of the Hilbert series, a weak confluence hypothesis isequivalent to some rather drastic conditions which determine the whole ofthe Hilbert series.

DOI: 10.1023/A:1009918131382
Print publication date: 9/1/1998
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