Standard and Non-standard Extensions of Lie algebras
نویسندگان
چکیده
We study the problem of quadruple extensions of simple Lie algebras. We find that, adding a new simple root α+4, it is not possible to have an extended Kac-Moody algebra described by a Dynkin-Kac diagram with simple links and no loops between the dots, while it is possible if α+4 is a Borcherds imaginary simple root. We also comment on the root lattices of these new algebras. The folding procedure is applied to the simply-laced triple extended Lie algebras, obtaining all the non-simply laced ones. Nonstandard extension procedures for a class of Lie algebras are proposed. It is shown that the 2-extensions of E8, with a dot simply linked to the Dynkin-Kac diagram of E9, are rank 10 subalgebras of E10. Finally the simple root systems of a set of rank 11 subalgebras of E11, containing as sub-algebra E10, are explicitly written. PACS numbers: 02.20.Tw, 11.30.Ly
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تاریخ انتشار 2005