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Holdaway, Cody Sisodia, Gautam
Published in
Journal of Algebra

Let k be a field, Q a finite directed graph, and kQ its path algebra. Make kQ an N-graded algebra by assigning each arrow a positive degree. Let I be an ideal in kQ generated by a finite number of paths and write A=kQ/I. Let QGrA denote the quotient of the category of graded right A-modules modulo the Serre subcategory consisting of those graded mo...

Jardim, Marcos Silva, Vitor
Published in
Open Mathematics

We establish a decomposability criterion for linear sheaves on ℙn. Applying it to instanton bundles, we show, in particular, that every rank 2n instanton bundle of charge 1 on ℙn is decomposable. Moreover, we provide an example of an indecomposable instanton bundle of rank 2n − 1 and charge 1, thus showing that our criterion is sharp.

Fahr, Philipp Ringel, Claus Michael
Published in
Advances in Mathematics

In two previous papers we have presented partition formulas for the Fibonacci numbers motivated by the appearance of the Fibonacci numbers in the representation theory of the 3-Kronecker quiver and its universal cover, the 3-regular tree. Here we show that the basic information can be rearranged in two triangles. They are quite similar to the Pasca...