Conformally invariant elliptic Liouville equation and its symmetry-preserving discretization

DOI10.1134/S0040577918090052zbMATH Open1409.35087arXiv1705.00491OpenAlexW2767854637MaRDI QIDQ1716288

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Publication date: 4 February 2019

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Abstract: The symmetry algebra of the real elliptic Liouville equation is an infinite-dimensional loop algebra with the simple Lie algebra $o(3,1)$ as its maximal finite-dimensional subalgebra. The entire algebra generates the conformal group of the Euclidean plane $E_2$. This infinite-dimensional algebra distinguishes the elliptic Liouville equation from the hyperbolic one with its symmetry algebra that is the direct sum of two Virasoro algebras. Following a discretisation procedure developed earlier, we present a difference scheme that is invariant under the group $O(3,1)$ and has the elliptic Liouville equation in polar coordinates as its continuous limit. The lattice is a solution of an equation invariant under $O(3,1)$ and is itself invariant under a subgroup of $O(3,1)$, namely the $O(2)$ rotations of the Euclidean plane.

Full work available at URL: https://arxiv.org/abs/1705.00491

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