Cluster algebras and the subalgebra constructibility of the seven-particle remainder function
Sign Up to like & getrecommendations! Published in 2019 at "Journal of High Energy Physics"
DOI: 10.1007/jhep01(2019)017
Abstract: A bstractWe review various aspects of cluster algebras and the ways in which they appear in the study of loop-level amplitudes in planar N=4$$ \mathcal{N}=4 $$ supersymmetric Yang-Mills theory. In particular, we highlight the different… read more here.
Keywords: subalgebra constructibility; algebras subalgebra; cluster algebras; seven particle ... See more keywords
Graded quantum cluster algebras of infinite rank as colimits
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DOI: 10.1016/j.jpaa.2017.12.014
Abstract: We provide a graded and quantum version of the category of rooted cluster algebras introduced by Assem, Dupont and Schiffler and show that every graded quantum cluster algebra of infinite rank can be written as… read more here.
Keywords: quantum cluster; infinite rank; cluster algebras; cluster ... See more keywords
Generators of rank 2 cluster algebras of affine types via linearization of seed mutations
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mathematical Physics"
DOI: 10.1063/1.5053429
Abstract: From the viewpoint of integrable systems on algebraic curves, we discuss linearization of birational maps arising from the seed mutations of types $A^{(1)}_1$ and $A^{(2)}_2$, which enables us to construct the set of all cluster… read more here.
Keywords: seed; integrable systems; seed mutations; curve ... See more keywords
Cluster Algebras for Feynman Integrals.
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DOI: 10.1103/physrevlett.126.091603
Abstract: We initiate the study of cluster algebras in Feynman integrals in dimensional regularization. We provide evidence that four-point Feynman integrals with one off-shell leg are described by a C_{2} cluster algebra, and we find cluster… read more here.
Keywords: algebras feynman; feynman integrals; cluster algebras; particle ... See more keywords
Unistructurality of cluster algebras
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DOI: 10.1112/s0010437x20007113
Abstract: We prove that any skew-symmetrizable cluster algebra is unistructural, which is a conjecture by Assem, Schiffler and Shramchenko. As a corollary, we obtain that a cluster automorphism of a cluster algebra ${\mathcal{A}}({\mathcal{S}})$ is just an… read more here.
Keywords: cluster; cluster algebras; unistructurality cluster;
Rogers dilogarithms of higher degree and generalized cluster algebras
Sign Up to like & getrecommendations! Published in 2018 at "Journal of the Mathematical Society of Japan"
DOI: 10.2969/jmsj/75767576
Abstract: In connection with generalized cluster algebras we introduce a certain generalization of the celebrated Rogers dilogarithm, which we call the Rogers dilogarithms of higher degree. We show that there is an identity of these generalized… read more here.
Keywords: rogers dilogarithms; higher degree; dilogarithms higher; generalized cluster ... See more keywords