Algebras with irreducible module varieties II: Two vertex case

2018/01/11 by Bobiński, Grzegorz, Schröer, Jan
#14M99 #14R99 #16G20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1801.03677

Abstract

We call a finite-dimensional K-algebra A geometrically irreducible if for all d all connected components of the affine scheme of d-dimensional A-modules are irreducible. We prove that a geometrically irreducible algebra with exactly two simple modules has to be of a very special form, which we describe. Based on this result we prove that every minimal geometrically irreducible algebra without shortcuts in its Gabriel quiver has at most two simple modules.

Related

• Algebras with irreducible module varieties I
• Two vertex geometrically irreducible algebras
• Irreducible components of varieties of modules
• Irreducible components of varieties of representations II
• Irreducible components of module varieties: projective equations and rationality