Zig
Apr7-04, 08:46 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no, location=no,scrollbars=yes,resize=yes,status=no,wi dth=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Alexander Kubelsky wrote:\n> The statement is that group of conformal trasformations in dimensions\n> higher than 2 have finite number of elements, and only in D=2 it have\n> infinite number of elements (analytic functions).\n> Where can I read about this in details ?\n>\n\nThe conformal group in D>2 has a finite number of dimensions as a Lie\ngroup or manifold. In this case, its dimension is (D+1)(D+2)/2. As any\nreal manifold of dimension greater than 0, it has a nondenumerable\ninfinity of elements, just like the real line. so the conformal group\ndoes not have a finite number of elements.\n\nthe difference between the D=2 case and the D>2 is that the D=2 is not\neven finitely generated.\n\nfor the details, see, for example, Di Francesco, Senechal, Mathieu,\n"Conformal Field theory", Springer Verlag.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Alexander Kubelsky wrote:
> The statement is that group of conformal trasformations in dimensions
> higher than 2 have finite number of elements, and only in D=2 it have
> infinite number of elements (analytic functions).
> Where can I read about this in details ?
>
The conformal group in D>2 has a finite number of dimensions as a Lie
group or manifold. In this case, its dimension is (D+1)(D+2)/2. As any
real manifold of dimension greater than 0, it has a nondenumerable
infinity of elements, just like the real line. so the conformal group
does not have a finite number of elements.
the difference between the D=2 case and the D>2 is that the D=2 is not
even finitely generated.
for the details, see, for example, Di Francesco, Senechal, Mathieu,
"Conformal Field theory", Springer Verlag.
> The statement is that group of conformal trasformations in dimensions
> higher than 2 have finite number of elements, and only in D=2 it have
> infinite number of elements (analytic functions).
> Where can I read about this in details ?
>
The conformal group in D>2 has a finite number of dimensions as a Lie
group or manifold. In this case, its dimension is (D+1)(D+2)/2. As any
real manifold of dimension greater than 0, it has a nondenumerable
infinity of elements, just like the real line. so the conformal group
does not have a finite number of elements.
the difference between the D=2 case and the D>2 is that the D=2 is not
even finitely generated.
for the details, see, for example, Di Francesco, Senechal, Mathieu,
"Conformal Field theory", Springer Verlag.