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dc.contributor.author
Ames, Guillermo
dc.contributor.author
Cagliero, Leandro Roberto
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dc.contributor.author
Cruz, Mónica Nancy
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dc.date.available
2023-01-26T13:16:49Z
dc.date.issued
2015-03
dc.identifier.citation
Ames, Guillermo; Cagliero, Leandro Roberto; Cruz, Mónica Nancy; Some remarks on graded nilpotent Lie algebras and the Toral Rank Conjecture; World Scientific; Journal of Algebra and its Applications; 14; 2; 3-2015; 1-13
dc.identifier.issn
0219-4988
dc.identifier.uri
http://hdl.handle.net/11336/185747
dc.description.abstract
If is a Zd+-graded nilpotent finite-dimensional Lie algebra over a field of characteristic zero, a well-known result of Deninger and Singhof states that dimH∗() ≥ L(p) where p is the polynomial associated to the grading and L(p) is the sum of the absolute values of the coefficients of p. From this result they derived the Toral Rank Conjecture (TRC) for 2-step nilpotent Lie algebras. An algebraic version of the TRC states that dimH∗() ≥ 2dim() for any finite-dimensional nilpotent Lie algebra with center. The TRC is more than 25 years old and remains open even for Zd+-graded 3-step nilpotent Lie algebras. Investigating to what extent the bound given by Deninger and Singhof could help to prove the TRC in this case, we considered the following two questions regarding a nilpotent Lie algebra with center : (A) If admits a Z+d-grading n = Z+d nα, such that its associated polynomial p satisfies L(p) > 2dim, does admit +-grading n = n1 ⊕ n2 ⊕ nk such that its associated polynomial p′ satisfies L(p′) > 2dim (B) If is r-step nilpotent admitting a grading n = n1• n2 Š• ⋯ nk such that its associated polynomial p satisfies L(p) > 2dim, does admit a grading n= n1 ⊕ n2 ⊕ ⊕ nr such that its associated polynomial p′ satisfies L(p′) > 2dim? In this paper we show that the answer to (A) is yes, but the answer to (B) is no.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
World Scientific
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
COHOMOLOGY OF LIE ALGEBRAS
dc.subject
GRADINGS
dc.subject
NILPOTENT LIE ALGEBRAS
dc.subject
TORAL RANK CONJECTURE
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Some remarks on graded nilpotent Lie algebras and the Toral Rank Conjecture
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2023-01-23T16:41:27Z
dc.identifier.eissn
1793-6829
dc.journal.volume
14
dc.journal.number
2
dc.journal.pagination
1-13
dc.journal.pais
Singapur
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dc.description.fil
Fil: Ames, Guillermo. Secretaria de Ciencia y Tecnica ; Facultad Regional Cordoba ; Universidad Tecnologica Nacional;
dc.description.fil
Fil: Cagliero, Leandro Roberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
dc.description.fil
Fil: Cruz, Mónica Nancy. Universidad Nacional de Salta. Facultad de Cs.exactas - Cons.de Investigación; Argentina
dc.journal.title
Journal of Algebra and its Applications
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.worldscientific.com/doi/10.1142/S0219498815500243
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1142/S0219498815500243
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