Abstract
Some observations and conjectures concerning finite dimensional associative commutative algebras that are degenerations of semisimple algebras.
“…on sait qu'on ne sait rien sur cette sorte d'algèbre.” André Weil
Keywords:
5. ACKNOWLEDGMENTS
The work was partially supported by grant of RFFI 00-01-00170.
Notes
I want to mention that in my earlier paper Citation[3] I had in mind “reduced at the generic point” when wrote “reduced” in the formulation of Theorem 1. Whether the schemes U n, r are reduced at other points seems an interesting question.
Many years ago A.V. Roiter showed me this algebra as an explicit example of a nilpotent algebra which is a degeneration of semisimple algebras.