Potentials and Jacobian algebras for tensor algebras of bimodules

Mathematics – Representation Theory

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

46 pages. New in this last version: the graded context has been considered. The actual length, 46 pages, rather than 55 pages

Scientific paper

We introduce and study potentials, mutations and Jacobian algebras in the framework of tensor algebras associated with symmetrizable dualizing pairs of bimodules on a symmetric algebra over any commutative ground ring. The graded context is also considered by starting from graded bimodules, and the classical non simply-laced context of modulated quivers with potentials is a particular case. The study of potentials in this framework is related to symmetrically separable algebras, and we have two kinds of potentials: the symmetric and the non symmetric ones. When the Casimir ideal of the symmetric algebra coincides with its center, all potentials appear as symmetric potentials and their manipulation mimics the simply laced study of quivers with potentials. This useful information suggests that, for applications to cluster algebras theory and related fields, one may restrict a further study of modulated quivers with potentials to the setting where the ground symmetric algebra is separable over a field. Associated with this work is a generalized construction of Ginzburg dg-algebras and cluster categories associated with graded modulated quivers with potentials.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

Potentials and Jacobian algebras for tensor algebras of bimodules 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 Potentials and Jacobian algebras for tensor algebras of bimodules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Potentials and Jacobian algebras for tensor algebras of bimodules will most certainly appreciate the feedback.

Rate now

     

Profile ID: LFWR-SCP-O-282653

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.