Homological invariants relating the super Jordan plane to the Virasoro algebra

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, th...

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Detalles Bibliográficos
Publicado: 2018
Materias:
Gerstenhaber bracket
Hochschild cohomology
Nichols algebra
Virasoro algebra
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v507_n_p120_Reca
http://hdl.handle.net/20.500.12110/paper_00218693_v507_n_p120_Reca
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00218693_v507_n_p120_Reca
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spelling paper:paper_00218693_v507_n_p120_Reca2023-06-08T14:42:30Z Homological invariants relating the super Jordan plane to the Virasoro algebra Gerstenhaber bracket Hochschild cohomology Nichols algebra Virasoro algebra 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 2018 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v507_n_p120_Reca http://hdl.handle.net/20.500.12110/paper_00218693_v507_n_p120_Reca
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Gerstenhaber bracket
Hochschild cohomology
Nichols algebra
Virasoro algebra
spellingShingle Gerstenhaber bracket
Hochschild cohomology
Nichols algebra
Virasoro algebra
Homological invariants relating the super Jordan plane to the Virasoro algebra
topic_facet Gerstenhaber bracket
Hochschild cohomology
Nichols algebra
Virasoro algebra
description 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
title Homological invariants relating the super Jordan plane to the Virasoro algebra
title_short Homological invariants relating the super Jordan plane to the Virasoro algebra
title_full Homological invariants relating the super Jordan plane to the Virasoro algebra
title_fullStr Homological invariants relating the super Jordan plane to the Virasoro algebra
title_full_unstemmed Homological invariants relating the super Jordan plane to the Virasoro algebra
title_sort homological invariants relating the super jordan plane to the virasoro algebra
publishDate 2018
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00218693_v507_n_p120_Reca
http://hdl.handle.net/20.500.12110/paper_00218693_v507_n_p120_Reca
_version_ 1768543356838739968

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