Multiplicative bases and standardness of representation-finite algebras
A complete Lean 4 formalization, built on Mathlib, of two classical theorems of Bautista, Gabriel, Roiter and Salmerón on finite-dimensional representation-finite algebras over an algebraically closed field. Theorem A: every such algebra, in any characteristic, has a normed multiplicative basis, that is, a basis containing a complete set of primitive orthogonal idempotents, closed under products up to zero, and meeting every power of the Jacobson radical in a basis of that power. Theorem B: every basic such algebra over a field of characteristic different from two is standard, that is, its…
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