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|ROSS WILLARD, Pure Mathematics Department, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada|
|Independence of the linear commutator|
Years ago, Lampe discovered some unexpected interactions between the congruence lattice of an algebra (as an abstract lattice) and the term-condition commutator operation on this lattice. We claim that no result of this kind is possible for the linear commutator. In particular, no lattice-theoretic property of the congruence lattice of an algebra can force the algebra to be quasi-affine. This is joint work with K. A. Kearnes (University of Louisville) and W. A. Lampe (University of Hawaii).