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G-Quadratic, LG-Quadratic, and Koszul Quotients of Exterior Algebras (2105.13457v1)
Published 27 May 2021 in math.RA and math.AC
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.
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