Centralizers in Free Group Algebras and Nonsingular Curves
Nikita Miasnikov
TL;DR
This paper shows that the centralizer of a non-scalar element in a free group algebra corresponds to the coordinate ring of a nonsingular curve, revealing a geometric structure underlying algebraic centralizers.
Contribution
It establishes a link between algebraic centralizers in free group algebras and the geometry of nonsingular curves, providing a new perspective on their structure.
Findings
Centralizers are coordinate rings of nonsingular curves.
Non-scalar elements have centralizers with geometric interpretation.
The result applies over any field for free group algebras.
Abstract
The centralizer of any non-scalar element of a free group algebra over a field is the coordinate ring of a nonsingular curve.
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