Incidence, or poset, algebras can be given a Lie structure by taking the commutator product. Curiously, these "Lie poset algebras" have only recently been introduced into the literature. Here, we initiate the study of the index of Lie poset subalgebras of \(A_n=\mathfrak{sl}(n+1)\) by providing combinatorial index formulas. Index-zero Lie algebras are called Frobenius and are of interest to those working in invariant and deformation theory. Using our new index formulas, we combinatorially characterize posets (of restricted height) which correspond to Frobenius type-A Lie poset algebras. The topical theory of the "spectrum" of these Frobenius type-A Lie poset algebras is also investigated. We conclude by showing how this theory can be extended to the other classical types.
Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.
The ACO Seminar (2019–2020)