Classification of Simple Graded Lie Algebras With Nonsemisimple Component $ L_0$

Abstract

The pressure dependence of the decay of the Ar(3p 5 4p) states excited by an energetic pulsed ion beam was studied in the pressure range 5-1600 kPa. All of the ten 3p 5 4p states have a fast build-up component and, with the exception of the 2p 1 state, two decay components: one fast (3-18 ns at 100 kPa) and one slow (20-300 ns at 100 kPa). Extrapolation of the fast decay rates to zero pressure yields the natural lifetimes of the states to values within the accuracy of the measurements. Most of the slow decays show nonlinear pressure dependencies. This nonlinearity is probably due to several competing processes. The slow decay of the 2p 3 -2p 5 states can be associated with the fast decay of the 2p 2 state. The pressure dependency of the 2p 2 state is considerably different from the other states within the 3p 5 4p configuration. It is concluded that the build-up of the 2p 2 state is associated with dissociative recombination of Ar + 2 and Ar 2+ 3 molecules. ¶

On the Structure of the Graded Lie Algebra Associated with a Noncontractible Filtration

“…There is much more information available w x on those algebras due to the work of M. I. Kuznetsov 11,12,14 . For our purposes it is absolutely necessary to have an extension of some of his results to the case of nonsimple graded Lie algebras.…”

Maximal subalgebras of the exceptional Lie algebras in low characteristic

“…Then, in addition with [KO95, Kuz89,Skr92] we are able to identify simple Lie algebras when they have depth-one gradings. We start with a recognition theorem for depth-one graded Lie algebras for p = 3.…”

Lie Algebras of CL Type

“…(2.17) Examples. The following Lie algebras are of CA type: (i) the nonexceptional (generalized) Cartan-type algebras, p > 0; (ii) the Melikyan algebras of characteristic 5 [M]; (iii) T n of characteristic 3 discussed in [B1,B2,Ch,Ku,Sk1]; (iv) R 2 n 1 n 2 1 of characteristic 3 discussed in [B2,Ch,E,Ku,Sk1]; (v) Z F , Y F , and X F ω of characteristic 3 in [Sk1];…”