Let K be a field of positive characteristic p and let UTp+1(K) be the algebra of (p+1)×(p+1) upper triangular matrices. We construct three varieties of ℤp+1-graded Lie algebras which do not have a finite basis of their graded identities and satisfy the graded identities which in the case of infinite field define the variety generated by UTp+1(K). The first variety contains the other two. The second one is locally finite. The third variety is generated by a finite dimensional algebra over an infinite field. These results are in the spirit of similar results obtained in the 1970s and 1980s for non-graded Lie algebras in positive characteristic.
This is a joint project with Plamen Koshlukov and Daniela Martinez Correa.
This video is part of the Non-Associative Day in Online, run by the European Non-Associative Algebra Seminar series.
