#### 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