arXiv · 0704.1892
I show that an (n+2)-dimensional n-Lie algebra over an algebraically closed field must have a subalgeba of codimension 1.
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Donald W. Barnes. 2007-04-15. On (n+2)-dimensional n-Lie algebras. https://arxiv.org/abs/0704.1892
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This paper introduces the structure of operated polygraphs as a categorical model for rewriting in operated algebras, generalizing Gröbner--Shirshov bases with non-monomial termination orders. We show how to construct polygraphic resolutions of free operated algebras from confluent and terminating presentations. We provide a combinatorial description of critical branchings of operated polygraphs using the structure of polyautomata introduced in this paper. Polyautomata are linear polygraphs equipped with an operator structure formalized by a pushdown automaton. Finally, we apply our constructions to several families of operated algebras, including Rota--Baxter algebras, differential algebras, and differential Rota--Baxter algebras.
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