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Abstract
This paper introduces the study of LG-quadratic quotients of exterior algebras, showing that they are Koszul, as in the commutative case. We construct an example of an LG-quadratic algebra that is not G-quadratic and another example that is Koszul but not LG-quadratic. This is only the second known Koszul algebra that is not LG-quadratic and the first that is noncommutative.
2020 Mathematics Subject Classification:
Acknowledgements
The authors thank Aldo Conca and Hal Schenck for useful conversations.
Additional information
Funding
The first author was supported by National Science Foundation grant DMS-1900792.