Lie Algebras Graded by the Root Systems BCr, R 2

Introduction The $/mathfrak{g}$-module decomposition of a $/mathrm{BC}_r$-graded Lie algebra, $r/ge 3$ (excluding type $/mathrm{D}_3)$ Models for $/mathrm{BC}_r$-graded Lie algebras, $r/ge 3$ (excluding type $/mathrm{D}_3)$ The $/mathfrak{g}$-module decomposition of a $/mathrm{BC}_r$-graded Lie algebra with grading subalgebra of type $/mathrm{B}_2$, $/mathrm{C}_2$, $/mathrm{D}_2$, or $/mathrm{D}_3$ Central extensions, derivations and invariant forms Models of $/mathrm{BC}_r$-graded Lie algebras with grading subalgebra of type $/mathrm{B}_2$, $/mathrm{C}_2$, $/mathrm{D}_2$, or $/mathrm{D}_3$ Appendix: Peirce decompositions in structurable algebras References.