Structure Of Cylindrical 2 - Membrane Lie Algebra

This thesis is a study on the structure theory of the cylindrical two-brane Lie algebra, which was introduced by physicist Kim and Rey in their study of M-theory of string theory in1997. It is defined as follows:Let C=⊕α∈Z+,m∈Z CLmα. The Lie bracket [·,·] on C is defined by where Lm0=0, Lm-α=-Lmα. In this paper, we determine all symmetric invariant bilinear forms, derivations, and central extensions of C.(1) Let Inv(C) denote the vector space of all symmetric invariant bilinear forms on C Then where φ1; φ2is defined by, for (?) m,n∈Z, α,β∈Z+(2) Let H1(C,C) denote the first cohomology group of C.Then where D is defined by (3) Let H2(C,C) denote the second cohomology group of C. Then where ψ is defined by...