Hochschild cohomology ring modulo nilpotence of a one point extension of a quiver algebra defined by two cycles and a quantum-like relation
Authors:
Daiki Obara
Affiliation:
Department of Mathematics, Tokyo University of Science, Shinjuku-ku, Tokyo, Japan
Abstract:
We consider a one point extension algebra B of a quiver algebra Aq over a field k defined by two cycles and a quantum-like relation depending on a nonzero element q in k. We determine the Hochschild cohomology ring of B modulo nilpotence and show that if q is a root of unity, then B is a counterexample to Snashall-Solberg’s conjecture.