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Some Generalized Kac-Moody Algebras with Known Root Multiplicities
Peter Niemann
出版
American Mathematical Soc.
, 2002
主題
Mathematics / Algebra / General
Mathematics / Algebra / Linear
ISBN
0821828886
9780821828885
URL
http://books.google.com.hk/books?id=Ys3UCQAAQBAJ&hl=&source=gbs_api
EBook
SAMPLE
註釋
Starting from Borcherds' fake monster Lie algebra, this text construct a sequence of six generalized Kac-Moody algebras whose denominator formulas, root systems and all root multiplicities can be described explicitly. The root systems decompose space into convex holes, of finite and affine type, similar to the situation in the case of the Leech lattice. As a corollary, we obtain strong upper bounds for the root multiplicities of a number of hyperbolic Lie algebras, including $AE_3$.