The Endomorphism Ring Theorem for Galois and D2 extensions

Details The Endomorphism Ring Theorem for Galois and D2 extensions The Endomorphism Ring Theorem for Galois and D2 extensions

2005-03-10

arxiv.org/abs/math/0503194v2

Mathematics

Quantum Algebra

20 pp, some additional material including a converse endomorphism ring theorem for certain Frobenius extensions, which yields

Scientific paper

Let $S$ 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.

Affiliated with

Also associated with

No associations

Rating

The Endomorphism Ring Theorem for Galois and D2 extensions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Endomorphism Ring Theorem for Galois and D2 extensions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Endomorphism Ring Theorem for Galois and D2 extensions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-685513