Parameter curves for the regular representations of tame bimodules

Mathematics – Representation Theory

Scientific paper

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13 pages, to appear in J. Algebra. Typos corrected

Scientific paper

10.1016/j.jalgebra.2008.05.022

We present results and examples which show that the consideration of a certain tubular mutation is advantageous in the study of noncommutative curves which parametrize the simple regular representations of a tame bimodule. We classify all tame bimodules where such a curve is actually commutative, or in different words, where the unique generic module has a commutative endomorphism ring. This extends results from [14] to arbitrary characteristic; in characteristic two additionally inseparable cases occur. Further results are concerned with autoequivalences fixing all objects but not isomorphic to the identity functor.

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