DEGENERATION OF SEMISIMPLE ALGEBRAS

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:

• Algebras
• Algebraic varieties
• Blowup

5. ACKNOWLEDGMENTS

The work was partially supported by grant of RFFI 00-01-00170.

Notes

I want to mention that in my earlier paper [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.