{VERSION 3 0 "IBM INTEL NT" "3.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 
1 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 
0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 
0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 }1 0 0 0 8 4 
0 0 0 0 0 0 -1 0 }}
{SECT 0 {SECT 1 {PARA 3 "" 0 "" {TEXT -1 14 "Initialization" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "with(liealg);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 69 "libname := \"C:\\\\Program Files\\\\Maple V Release 5
\\\\Lie\\\\Lib\", libname;" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 
1 {PARA 3 "" 0 "" {TEXT -1 16 "Free Lie algebra" }}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 22 "generators(L,[x,y,z]);" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 15 "simplify(y&*x);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "a:=x&*y; b:=y&*z;" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 15 "simplify(a&*b);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 9 "wt(a&*b);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
22 "genhallmon([1,2,1],L);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 
1 {PARA 3 "" 0 "" {TEXT -1 37 "Free Lie algebra with another grading" 
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "generators(L2,[x,y,z],[[1]
,[1],[1]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "use(L2);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "wt(((x&*y)&*z)&*x);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "genhallmon([4],L2);" }}}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 5 "sl(2)" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 39 "generators(sl2,[e,h,f],[[1],[0],[-1]]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "use(sl2);" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 35 "store([h&*e=2*e,h&*f=-2*f,e&*f=h]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "simplify((e&*f)&*(e+f));" }}}{PARA 
0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 16 "Viraso
ro algebra" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 33 "generators(V,[e[i],z],[[i],[0]]);" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 7 "use(V);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 60 "store([e[i]&*e[j]=(j-i)*e[i+j]+delta[i,-j]*i*z, e[i]&
*z=0]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "simplify(e[3]&*e
[-3]);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 34 "Simple finite-dimensi
onal algebras" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "simple(F,F[
4]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "use(F);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "eval(A_F);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 33 "simplify(e[1,0,0,0]&*e[0,1,0,0]);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "simplify(e[1,1,1,1]&*e[1,1,0,0]);" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "simplify(e[2,2,1,1]&*e[1,
0,0,0]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "simplify(e[-1,-
2,-1,-1]&*e[1,2,1,1]);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 37 "Factor-algebras of a free Lie algebra" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "generators(P,[x,y]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "use(P);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 41 "ideal(K,[x&*(x&*(x&*y)),((x&*y)&*y)&*y]);" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "factoralg(S,[P,K]);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "use(S);" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 32 "simplify(x&*(y&*(x&*(y&*x))),S);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "genbasis([3,2],S);" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "genbasis([4,2],S);" }}}{PARA 0 "" 
0 "" {TEXT -1 0 "" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 18 "Kac-Moody a
lgebras" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 22 "restart; with(liealg):" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 27 "C:=matrix([[2,-3],[-3,2]]);" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 14 "KacMoody(G,C);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 14 "generators(G);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 7 "use(G);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "simplify(
((((e[1]&*e[2])&*e[1])&*e[2])&*f[1]),G);" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 47 "simplify(e[1]&*(e[1]&*(e[1]&*(e[1]&*e[2]))),G);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "genbasis([4,4],G_plus);" }}}
}}{MARK "0" 0 }{VIEWOPTS 1 1 0 1 1 1803 }