The Endomorphism Ring Theorem for Galois and D2 extensions

dc.creatorKadison, Lars
dc.date2005-03-10
dc.date2005-04-01
dc.date.accessioned2026-07-07T05:17:51Z
dc.date.available2026-07-07T05:17:51Z
dc.descriptionLet $S$ be the left bialgebroid $\End {}_BA_B$ 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. We prove that its left endomorphism algebra is a left $S$-Galois extension of $A^{\rm op}$. As a corollary, endomorphism ring theorems for D2 and Galois extensions are derived from the D2 characterization of Galois extension (cf. math.QA/0502188 and math.QA/0409589). We note the converse that a Frobenius extension satisfying a generator condition is D2 if its endomorphism algebra extension is D2.
dc.description20 pp, some additional material including a converse endomorphism ring theorem for certain Frobenius extensions, which yields a complete answer to question 1 in math.RA/0107064
dc.identifierhttps://arxiv.org/abs/math/0503194
dc.identifierhttp://arxiv.org/abs/math/0503194
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/74457
dc.subjectQuantum Algebra
dc.subject13B05, 16S40, 20L05, 81R50
dc.titleThe Endomorphism Ring Theorem for Galois and D2 extensions
dc.typetext

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