Homological invariants relating the super Jordan plane to the Virasoro algebra

JOURNAL OF ALGEBRA

卷:507

Article

Reca, Sebastian^1,2  Solotar, Andrea^1,2 

[1] Univ Buenos Aires, Fac Ciencias Exactas & Nat, Dept Matemat, Ciudad Univ,Pabellon 1, RA-1428 Buenos Aires, DF, Argentina

[2] UBA, CONICET, IMAS, Ciudad Univ,Pabellon 1, RA-1428 Buenos Aires, DF, Argentina

关键词: Nichols algebra;    Hochschild cohomology;    Virasoro algebra;    Gerstenhaber bracket;   

DOI  :  10.1016/j.jalgebra.2018.04.008

来源: Elsevier

【 摘 要 】

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 = 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 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 not equal kZ of A is also finitely generated, but not K-2. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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