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dc.contributor.author
Lebed, Victoria
dc.contributor.author
Vendramin, Claudio Leandro
dc.date.available
2018-08-15T04:05:07Z
dc.date.issued
2017-01
dc.identifier.citation
Lebed, Victoria; Vendramin, Claudio Leandro; Homology of left non-degenerate set-theoretic solutions to the Yang–Baxter equation; Academic Press Inc Elsevier Science; Advances in Mathematics; 304; 1-2017; 1219-1261
dc.identifier.issn
0001-8708
dc.identifier.uri
http://hdl.handle.net/11336/55537
dc.description.abstract
This paper deals with left non-degenerate set-theoretic solutions to the Yang–Baxter equation (= LND solutions), a vast class of algebraic structures encompassing groups, racks, and cycle sets. To each such solution there is associated a shelf (i.e., a self-distributive structure) which captures its major properties. We consider two (co)homology theories for LND solutions, one of which was previously known, in a reduced form, for biracks only. An explicit isomorphism between these theories is described. For groups and racks we recover their classical (co)homology, whereas for cycle sets we get new constructions. For a certain type of LND solutions, including quandles and non-degenerate cycle sets, the (co)homologies split into the degenerate and the normalized parts. We express 2-cocycles of our theories in terms of group cohomology, and, in the case of cycle sets, establish connexions with extensions. This leads to a construction of cycle sets with interesting properties.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Academic Press Inc Elsevier Science
dc.rights
info:eu-repo/semantics/restrictedAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Birack
dc.subject
Braided Homology
dc.subject
Cubical Homology
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Cycle Set
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Extension
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Quandle
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Rack
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Shelf
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Yang–Baxter Equation
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
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CIENCIAS NATURALES Y EXACTAS
dc.title
Homology of left non-degenerate set-theoretic solutions to the Yang–Baxter equation
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2018-08-14T13:57:42Z
dc.journal.volume
304
dc.journal.pagination
1219-1261
dc.journal.pais
Países Bajos
dc.journal.ciudad
Amsterdam
dc.description.fil
Fil: Lebed, Victoria. Trinity College Dublin; Irlanda
dc.description.fil
Fil: Vendramin, Claudio Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
dc.journal.title
Advances in Mathematics
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.aim.2016.09.024
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/pii/S0001870815302851
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