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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 189, Number 3, Pages 380–388
DOI: https://doi.org/10.4213/tmf9252 (Mi tmf9252) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Cyclic gradings of Lie algebras and Lax pairs for $\sigma$-models

D. V. Bykov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Full-text PDF (483 kB) Citations (8)
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DOI: https://doi.org/10.4213/tmf9252
Abstract: We study a class of $\sigma$-models with complex homogeneous target spaces and zero-curvature representations. We find a relation between these models and $\sigma$-models with certain $m$-symmetric target spaces. We also describe a model with the hypercomplex target space $S^1\times S^3$ in detail.
Keywords: $\sigma$-model, integrable system, complex structure.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.
Received: 11.07.2016
English version:
Theoretical and Mathematical Physics, 2016, Volume 189, Issue 3, Pages 1734–1741
DOI: https://doi.org/10.1134/S0040577916120060
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: D. V. Bykov, “Cyclic gradings of Lie algebras and Lax pairs for $\sigma$-models”, TMF, 189:3 (2016), 380–388; Theoret. and Math. Phys., 189:3 (2016), 1734–1741
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/tmf/v189/i3/p380
    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:65
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