  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.
