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 ...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.展开更多
文摘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.
