# PBW deformations of a Fomin-Kirillov algebra and other examples

## TL;DR

This paper investigates PBW deformations of graded algebras related to Hopf algebras, including the Fomin-Kirillov algebra FK3, providing criteria for semisimplicity and constructing PBW bases and polynomial identities.

## Contribution

It introduces new methods to analyze PBW deformations of specific graded algebras, including criteria for semisimplicity and explicit construction of PBW bases.

## Key findings

- Determined conditions for semisimplicity of deformations
- Constructed PBW bases for studied algebras
- Derived polynomial identities for the deformations

## Abstract

We begin the study of PBW deformations of graded algebras relevant to the theory of Hopf algebras. One of our examples is the Fomin-Kirillov algebra FK3. Another one appeared in a paper of Garc\'ia Iglesias and Vay. As a consequence of our methods, we determine when the deformations are semisimple and we are able to produce PBW bases and polynomial identities for these deformations.