PBW deformations of a Fomin-Kirillov algebra and other examples

Authors :: Heckenberger, I.
Vendramin, L.
Source :: Algebr. Represent. Theory 22 (2019), no. 6, 1513-1532
Publication Year :: 2017
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.<br />Comment: 22 pages. Accepted for publication in Algebr. Represent. Theory