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Abstract:

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 Hn(A,A) and also the Yoneda algebra. We prove that the algebra A is K2. Moreover, we prove that the Yoneda algebra of the bosonization A#kZ of A is also finitely generated, but not K2. © 2018

Registro:

Documento: Artículo
Título:Homological invariants relating the super Jordan plane to the Virasoro algebra
Autor:Reca, S.; Solotar, A.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
IMAS, UBA-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Ciudad Universitaria, Pabellón I, Buenos Aires, 1428, Argentina
Palabras clave:Gerstenhaber bracket; Hochschild cohomology; Nichols algebra; Virasoro algebra
Año:2018
Volumen:507
Página de inicio:120
Página de fin:185
DOI: http://dx.doi.org/10.1016/j.jalgebra.2018.04.008
Título revista:Journal of Algebra
Título revista abreviado:J. Algebra
ISSN:00218693
CODEN:JALGA
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v507_n_p120_Reca

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Citas:

---------- APA ----------
Reca, S. & Solotar, A. (2018) . Homological invariants relating the super Jordan plane to the Virasoro algebra. Journal of Algebra, 507, 120-185.
http://dx.doi.org/10.1016/j.jalgebra.2018.04.008
---------- CHICAGO ----------
Reca, S., Solotar, A. "Homological invariants relating the super Jordan plane to the Virasoro algebra" . Journal of Algebra 507 (2018) : 120-185.
http://dx.doi.org/10.1016/j.jalgebra.2018.04.008
---------- MLA ----------
Reca, S., Solotar, A. "Homological invariants relating the super Jordan plane to the Virasoro algebra" . Journal of Algebra, vol. 507, 2018, pp. 120-185.
http://dx.doi.org/10.1016/j.jalgebra.2018.04.008
---------- VANCOUVER ----------
Reca, S., Solotar, A. Homological invariants relating the super Jordan plane to the Virasoro algebra. J. Algebra. 2018;507:120-185.
http://dx.doi.org/10.1016/j.jalgebra.2018.04.008