This should be specified on the Visa. That having been said, you should be able to do what the principal visa holder is doing. So, if your wife has a work visa, you should be able to work too.
Still, visa regulations are tricky and often change. I would ask the embassy in writing what your rights are.
Best of luck
To start off with, have a look at our Visas for Germany and Work Permits for Germany pages.
Once you have done this, and have a general idea of how the system works, you should look at the German Ministry of the Interior's site, since there will be specific laws around seeking asylum.