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math.GR2025
Exposure Orders in Free Group Algebras: Minimal Schreier Transversals, Free Bases, and Gröbner Bases
Matan Seidel
Consider the free group algebra , where is a free group and a field. A well-order on is called an exposure order if words are greater than thei…
math.GR2025
Primitivity Testing in Free Group Algebras via Duality
Matan Seidel, Danielle Ernst-West, Doron Puder
Let be a field and a free group. By a classical result of Cohn and Lewin, the free group algebra is a free ideal ring (FIR): a ring over which the submodu…
math.GR2023
Stable Invariants of Words from Random Matrices
Doron Puder, Yotam Shomroni, Danielle Ernst-West +1
Let be a word in a free group. A few years ago, Magee and the first named author discovered that the stable commutator length (scl) of , a well-known topological invariant,…