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Register a new userRealizations of BC_r graded intersection matrix algebras with grading subalgebras of type B_r, $r geq 3$
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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 $chi$.
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The purpose of this paper is to determine all maximal graded subalgebras of the four infinite series of finite-dimensional graded Lie superalgebras of odd Cartan type over an algebraically closed field of characteristic $p>3$. All maximal graded subalgebras consist of three types (MyRoman{1}), (MyRoman{2}) and (MyRoman{3}). Maximal graded subalgebras of type (MyRoman{3}) fall into reducible maximal graded subalgebras and irreducible maximal graded subalgebras. In this paper we classify maximal graded subalgebras of types (MyRoman{1}), (MyRoman{2}) and reducible maximal g raded subalgebras.The classification of irreducible maximal graded subalgebras is reduced to that of the irreducible maximal subalgebras of the classical Lie superalgebra $mathfrak{p}(n)$.
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