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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Autores principales: Reca, S., Solotar, A.
Formato: JOUR
Materias:
Gerstenhaber bracket
Hochschild cohomology
Nichols algebra
Virasoro algebra
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00218693_v507_n_p120_Reca
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00218693_v507_n_p120_Reca2023-10-03T14:21:36Z Homological invariants relating the super Jordan plane to the Virasoro algebra Reca, S. Solotar, A. 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 JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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
Reca, S.
Solotar, A.
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
format JOUR
author Reca, S.
Solotar, A.
author_facet Reca, S.
Solotar, A.
author_sort Reca, S.
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
url http://hdl.handle.net/20.500.12110/paper_00218693_v507_n_p120_Reca
work_keys_str_mv AT recas homologicalinvariantsrelatingthesuperjordanplanetothevirasoroalgebra
AT solotara homologicalinvariantsrelatingthesuperjordanplanetothevirasoroalgebra
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