# Cohomology of some local selfinjective algebras

## TL;DR

This paper proves that the cohomology of certain 2-generated selfinjective algebras, including specific algebras from Hopf algebra classifications, is finitely generated, advancing understanding in algebraic cohomology.

## Contribution

It demonstrates finite generation of cohomology for a class of 2-generated selfinjective algebras, including algebras from the classification of connected Hopf algebras.

## Key findings

- Cohomology of some 2-generated selfinjective algebras is finitely generated.
- Application to algebras $A5(eta)$ with $eta
eq 0$ in Hopf algebra classification.
- Supports broader conjectures on cohomology finiteness in algebra.

## Abstract

We show that the cohomology for some 2-generated selfinjective algebras is finitely generated. This applies in particular to the algebras $A5(\beta)$ for $\beta\neq 0$ in the classification of connected Hopf algebras of dimension $p^3$ over characteristic $p$ by Nguyen-Wang-Wang.