Parameter curves for the regular representations of tame bimodules

TL;DR

This paper investigates the structure of noncommutative curves associated with tame bimodules, classifies when these curves are commutative, and explores autoequivalences that fix objects but are not the identity.

Contribution

It extends classification results of tame bimodules and their associated curves to arbitrary characteristic, including inseparable cases in characteristic two.

Findings

Classified tame bimodules with commutative parameter curves

Extended previous results to arbitrary characteristic

Analyzed autoequivalences fixing objects but not being the identity

Abstract

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.