Alladi Ramakrishnan Hall
Hilbert series of partially commutative Lie algebras
R. Venkatesh
IIT Madras
Let G be a finite simple graph with the vertex set V and the Edge
set E . Partially commutative Lie algebra 𝓅 (G) associated to G is the Lie
algebra freely generated by the variable Xi, i∈ V subject to the relations
[Xi, Xj]=0 for (i, j)∉ E. We will realize 𝓅 (G) as a subalgebra (positive
part) of Borcherds-Kac-Moody algebra and use the celebrated denominator
identity of Borcherds-Kac-Moody algebras to compute Hilbert series of 𝓅 (G)
in terms of independent set polynomial of G.
Done