Homological invariants relating the super Jordan plane to the Virasoro algebra

SEBASTIÁN RECA; ANDREA SOLOTAR

JOURNAL OF ALGEBRA

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2018 vol. 507 p. 120 - 185

0021-8693

Nichols algebras are an important tool for the classication of Hopf algebras. Within those with finite GK dimension, we study homological invariants of the super Jordan plane. These invariants are Hochschild homology, the Hochschild cohomology algebra, the Lie structure of the first cohomology space - which is a Lie subalgebra of the Virasoro algebra - and itsrepresentations H^n(A;A) and also the Yoneda algebra. We prove that the algebra A is K_2. Moreover, we prove that the Yoneda algebra of the bosonization A#kZ of A is also finitely generated, but not K_2. https://doi.org/10.1016/j.jalgebra.2018.04.008