Electrical Networks and Electrical Lie Theory of Classical Types by Yi Su Pdf, In this thesis we explore the arrangement of electric Lie algebras of finite Dynkin type. These Lie algebras were introduced by Lam-Pylyavskyy from the analysis of circular planar electric networks. One of these electric Lie algebras, the Lie group corresponding to kind A electric Lie algebra acts on these networks through a few combinatorial operations studied by Curtis-Ingerman-Morrow and Colin p Verdi`ere-Gitler-Vertigan. Lam-Pylyavskyy analyzed the kind A electric Lie algebra of rank in detail, also gave a conjecture for the measurement of electric Lie algebras of finite Dynkin forms.
We prove this conjecture for most classical Dynkin forms, in other words, B, A, C, and D. Moreover, we can explicitly clarify the arrangement of some electric Lie algebras of ancient forms as the semisimple merchandise of the symplectic Lie algebra with its finite dimensional irreducible representations. These mirror symmetric networks could be seen as the kind B generalization of round planar electric networks. We show that the Majority of the attributes of circular planar electric
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