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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 $r \geq 3$. We show that im(A^d) is isomorphic to the universal covering algebra of $so_{2r+1}(a,\eta,C,\chi)$, 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 $\chi$.

pacific journal of mathematics

Realizations ofBCr-graded intersection matrix algebras with grading subalgebras of typeBr,r≥ 3