Two separable algebras over a field are Morita equivalent iff they have an invertible bimodule. If it exists, is this bimodule unique (up to something)?
2026-03-25 18:48:11.1774464491
uniqueness of Morita equivalence bimodule
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No, because there exist separable algebras with many autoequivalences. The group of autoequivalences of an algebra is called the Picard group and it is very often non trivial.
Consider the product A of two copies of the ground field. There are two isomorphism classes of invertible A-bimodules.