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Left-Symmetric Algebra Structures on the Planar Galilean Conformal Algebra
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In this paper, we mainly determine the compatible left-symmetric algebra structures on the planar Galilean conformal algebra with some natural grading conditions. The results of earlier work on left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra play an important role in determining these compatible structures. As a corollary, any such left-symmetric algebra contains an infinite-dimensional non-trivial subalgebra that is also a submodule of the regular module.
Title: Left-Symmetric Algebra Structures on the Planar Galilean Conformal Algebra
Description:
In this paper, we mainly determine the compatible left-symmetric algebra structures on the planar Galilean conformal algebra with some natural grading conditions.
The results of earlier work on left-symmetric algebra structures on the twisted Heisenberg-Virasoro algebra play an important role in determining these compatible structures.
As a corollary, any such left-symmetric algebra contains an infinite-dimensional non-trivial subalgebra that is also a submodule of the regular module.
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