Invariantes homológicos del super plano de Jordan y su relación con el álgebra de Virasoro

SEBASTIÁN RECA; ANDREA SOLOTAR

Buenos Aires

Congreso; XXIV Encuentro Rioplatense de Álgebra y Geometría; 2017

Universidad Nacional de San Martín

Nichols algebras are an important tool for the classification  of Hopf algebras. Within those with finite $\GK$ dimension, we study homological invariants of the super Jordan plane, that is, the Nichols algebra $A = \mathfrak{B}(V(-1,2))$. 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 its representations $\Hy^{n}(A, A)$ and also the Yoneda algebra.    We prove that  the algebra $A$ is $\mathcal{K}_2$. Moreover, we prove that the Yoneda algebra of the bosonization  $A\#\field\ZZ$ of $A$ is also finitely generated, but not $\mathcal{K}_2$.