ar X iv : 0 80 8 . 24 23 v 1 [ m at h . Q A ] 1 8 A ug 2 00 8 Graphs , Frobenius functionals , and the classical Yang - Baxter equation
نویسنده
چکیده
A Lie algebra g is Frobenius if it admits a linear functional F ∈ g * such that the Kirillov form BF (x, y) = F ([x, y]) is non-degenerate. If g is the mth maximal parabolic subalgebra P(n, m) of sl(n) this occurs precisely when (n, m) = 1. We define a cyclic functional F on P(n, m) and prove it is non-degenerate using properties of graphs associated to F. These graphs also provide in certain cases readily computable associated solutions of the classical Yang-Baxter equation. We define the full local ring of a graph from which we show that the graph can be reconstructed (as well as a reduced local ring), consider the seaweed algebras of Dergachev and Kirillov, and examine the degeneration of solutions to the modified classical Yang-Baxter equation.
منابع مشابه
ar X iv : 0 80 8 . 23 49 v 1 [ m at h . N A ] 1 8 A ug 2 00 8 EULERIAN NUMBERS AND B SPLINES
2000 Mathematics Subject Classification. Primary 65D07; Secondary 11B68.
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تاریخ انتشار 2008