The Endomorphism Ring Theorem for Galois and D2 Extensions
نویسنده
چکیده
Let S be the left bialgebroid End BAB over the centralizer R of a right D2 algebra extension A | B, which is to say that its tensor-square is isomorphic as A-B-bimodules to a direct summand of a finite direct sum of A with itself. Without an antipode, we prove that the left endomorphism algebra is a left S-Galois extension of A, and find a formula for the inverse Galois mapping. As a corollary, we derive endomorphism ring theorems for one-sided D2 and Galois extensions from the D2 characterization of Galois extension [8, 9].
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