3-manifold group algebras and division rings
Revisiting Fundamental Problems Workshop: Infinite-Dimensional Division Algebras - Algebraicity and Freeness December 01, 2025 - December 05, 2025
Location: SLMath: Eisenbud Auditorium, Online/Virtual
Primary Mathematics Subject Classification
No Primary AMS MSC
Secondary Mathematics Subject Classification
No Secondary AMS MSC
3-manifold group algebras and division rings
The Kaplansky zero divisor conjecture predicts that if G is a torsion-free group and k is a field, then the group algebra k[G] is a domain. In this talk, we will survey history and progress on this conjecture, with a special emphasis on the related problem of embedding group algebras in division rings. We will also give new examples of group algebras embedding into division rings, such as fundamental groups of 3-manifolds, and thus verify the Kaplansky zero divisor conjecture for this class. Joint work with Pablo Sánchez-Peralta.
3-manifold group algebras and division rings
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