Realizations of BC_r graded intersection matrix algebras with grading subalgebras of type B_r, $r\ge 3$

Abstract

We study intersection matrix algebras im(A^d) that arise from affinizing a Cartan matrix A of type B_r with d arbitrary long roots in the root system ${\Delta }_{B_r}$, where $r\ge 3$. We show that im(A^d) is isomorphic to the universal covering algebra of $s{o}_{2r+1}(a,\eta ,C,\chi )$, where $a$ is an associative algebra with involution $\eta$, and $C$ is an $a$-module with hermitian form $\chi$. We provide a description of all four of the components $a$, $\eta$, $C$, and $\chi$.

46 pages; some revisions made including a more direct proof of Theorem 1

Cited by in corpus (1)

• A class of Lie algebras arising from intersection matrices