12,665 research outputs found
Inner Ideals of Simple Locally Finite Lie Algebras
Inner ideals of simple locally finite dimensional Lie algebras over an
algebraically closed field of characteristic 0 are described. In particular, it
is shown that a simple locally finite dimensional Lie algebra has a non-zero
proper inner ideal if and only if it is of diagonal type. Regular inner ideals
of diagonal type Lie algebras are characterized in terms of left and right
ideals of the enveloping algebra. Regular inner ideals of finitary simple Lie
algebras are described
Cartan subalgebras of root-reductive Lie algebras
Root-reductive Lie algebras are direct limits of finite-dimensional reductive
Lie algebras under injections which preserve the root spaces. It is known that
a root-reductive Lie algebra is a split extension of an abelian Lie algebra by
a direct sum of copies of finite-dimensional simple Lie algebras as well as
copies of the three simple infinite-dimensional root-reductive Lie algebras
sl_infty, so_infty, and sp_infty. As part of a structure theory program for
root-reductive Lie algebras, Cartan subalgebras of the Lie algebra gl_infty
were introduced and studied in a paper of Neeb and Penkov.
In the present paper we refine and extend the results of [N-P] to the case of
a general root-reductive Lie algebra g. We prove that the Cartan subalgebras of
g are the centralizers of maximal toral subalgebras and that they are nilpotent
and self-normalizing. We also give an explicit description of all Cartan
subalgebras of the simple Lie algebras sl_infty, so_infty, and sp_infty.
We conclude the paper with a characterization of the set of conjugacy classes
of Cartan subalgebras of the Lie algebras gl_infty, sl_infty, so_infty, and
sp_infty with respect to the group of automorphisms of the natural
representation which preserve the Lie algebra.Comment: 28 pages, 1 figur
On an approach to constructing static ball models in General Relativity
An approach to construction of static models is demonstrated for a fluid
ball. Five examples are considered. Two of them are exact solutions of the
Einstein equations; the other three are connected with the Airy special
functions, the hypergeometric functions and the Heun functions.Comment: 3 pages, Talk given at the International Conference RUSGRAV-14, June
27--July 4, 2011, Ulyanovsk, Russi
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