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The 2-group of symmetries of a split chain complex
dc.contributor.author | Elgueta Montó, Josep |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II |
dc.date.accessioned | 2011-04-19T09:49:57Z |
dc.date.available | 2011-04-19T09:49:57Z |
dc.date.issued | 2010-12-15 |
dc.identifier.uri | http://hdl.handle.net/2117/12410 |
dc.description.abstract | We explicitly compute the 2-group of self-equivalences and (homotopy classes of) chain homotopies between them for any {\it split} chain complex $A_{\bullet}$ in an arbitrary $\kb$-linear abelian category ($\kb$ any commutative ring with unit). In particular, it is shown that it is a {\it split} 2-group whose equivalence class depends only on the homology of $A_{\bullet}$, and that it is equivalent to the trivial 2-group when $A_\bullet$ is a split exact sequence. This provides a description of the {\it general linear 2-group} of a Baez and Crans 2-vector space over an arbitrary field $\mathbb{F}$ and of its generalization to chain complexes of vector spaces of arbitrary length. |
dc.format.extent | 23 p. |
dc.language.iso | eng |
dc.relation.ispartofseries | MAII-IR-10-00003 |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria K |
dc.subject.lcsh | K-theory |
dc.subject.lcsh | Homology theory |
dc.title | The 2-group of symmetries of a split chain complex |
dc.type | External research report |
dc.subject.lemac | K-teoria |
dc.subject.lemac | Homologia |
dc.contributor.group | Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions |
dc.subject.ams | Classificació AMS::19 K-theory |
dc.rights.access | Open Access |
local.identifier.drac | 5479960 |
dc.description.version | Preprint |
local.personalitzacitacio | true |
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