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Lie Algebras Graded by the Root Systems BC\(_r\), \(r\geq 2\)
Bruce Allison, University of Alberta, Edmonton, AB, Canada, Georgia Benkart, University of Wisconsin, Madison, WI, and Yun Gao, York University, Toronto, ON, Canada
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Memoirs of the American Mathematical Society
2002; 158 pp; softcover
Volume: 158
ISBN-10: 0-8218-2811-8
ISBN-13: 978-0-8218-2811-3
List Price: US$62
Individual Members: US$37.20
Institutional Members: US$49.60
Order Code: MEMO/158/751
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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
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