Memoirs of the American Mathematical Society 2002; 158 pp; softcover Volume: 158 ISBN10: 0821828118 ISBN13: 9780821828113 List Price: US$62 Individual Members: US$37.20 Institutional Members: US$49.60 Order Code: MEMO/158/751
 We classify the Lie algebras of characteristic zero graded by the finite nonreduced root systems \(\mathrm{BC}_r\) for \(r \geq 2\) and determine their derivations, central extensions, and invariant forms. Readership Graduate students and research mathematicians interested in nonassociative rings and algebras. Table of Contents  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
