The amsfonts style option will give you
access to the \frak and \Bbb fonts and will also
use the extra Computer Modern fonts from the AMS in order to provide
better access to bold math characters at smaller sizes and in
super- and subscripts.
AMSFonts typefaces.
With the AMSFonts installed and in use through either the amsfonts or
amssymb style option, the \frak and \Bbb commands
are available. \frak switches to the AMS Fraktur font, while
\Bbb switches to the so-called ``Blackboard Bold'' font.
Only uppercase letters are available in Blackboard Bold, and there is
no bold version of the font. Fraktur has both uppercase and lowercase letters
and will become bold in a bbox.
Here are the letters ``ABCDE'' from \frak: 
.
And here are the letters ``RIZN'' from \Bbb: 
.
Here is some math with superscripts and \frak. It demonstrates
the output of \bbox{#1}.
You do not have the amsfonts or amssymb option
selected, therefore the characters in the AMSFonts will not be
printed using \frak and \Bbb.