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Constructions of L∞ Algebras and Their Field Theory Realizations
Joint Authors
Hohm, Olaf
Kupriyanov, Vladislav
Lüst, Dieter
Traube, Matthias
Source
Advances in Mathematical Physics
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-11-01
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We construct L∞ algebras for general “initial data” given by a vector space equipped with an antisymmetric bracket not necessarily satisfying the Jacobi identity.
We prove that any such bracket can be extended to a 2-term L∞ algebra on a graded vector space of twice the dimension, with the 3-bracket being related to the Jacobiator.
While these L∞ algebras always exist, they generally do not realize a nontrivial symmetry in a field theory.
In order to define L∞ algebras with genuine field theory realizations, we prove the significantly more general theorem that if the Jacobiator takes values in the image of any linear map that defines an ideal there is a 3-term L∞ algebra with a generally nontrivial 4-bracket.
We discuss special cases such as the commutator algebra of octonions, its contraction to the “R-flux algebra,” and the Courant algebroid.
American Psychological Association (APA)
Hohm, Olaf& Kupriyanov, Vladislav& Lüst, Dieter& Traube, Matthias. 2018. Constructions of L∞ Algebras and Their Field Theory Realizations. Advances in Mathematical Physics،Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1119342
Modern Language Association (MLA)
Hohm, Olaf…[et al.]. Constructions of L∞ Algebras and Their Field Theory Realizations. Advances in Mathematical Physics No. 2018 (2018), pp.1-11.
https://search.emarefa.net/detail/BIM-1119342
American Medical Association (AMA)
Hohm, Olaf& Kupriyanov, Vladislav& Lüst, Dieter& Traube, Matthias. Constructions of L∞ Algebras and Their Field Theory Realizations. Advances in Mathematical Physics. 2018. Vol. 2018, no. 2018, pp.1-11.
https://search.emarefa.net/detail/BIM-1119342
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1119342