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arXiv · 1908.03105

Combinatorial index formulas for Lie algebras of seaweed type

Alex Cameron·Vincent E. Coll, Jr.·Matthew Hyatt
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Abstract

Analogous to the types A, B, and C cases, we address the computation of the index of seaweed subalgebras in the type-D case. Formulas for the algebra's index can be computed by counting the connected components of its associated meander. We focus on a set of distinguished vertices of the meander, called the tail of the meander, and using the tail, we provide comprehensive combinatorial formulas for the index of a seaweed in all the classical types. Using these formulas, we provide all general closed-form index formulas where the index is given by a polynomial greatest common divisor formula in the sizes of the parts that define the seaweed.

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Alex Cameron, Vincent E. Coll, Jr., Matthew Hyatt. 2019-08-08. Combinatorial index formulas for Lie algebras of seaweed type. https://arxiv.org/abs/1908.03105

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