Is it possible to control high current with small rms voltage?
Do you think that this is gonna work?
First a word of warning: Please respect the 110V mains supply, it can be lethal.
Dimming of a lightbulb works like: Dimmer to bulb control
The below two links describe a method with a zero crossing circuit and a triac to control a lightbulb from Arduino (or most any microcontroller). The controller is synchronized to the mains supply by a zero crossing detector and in turn fires the triac at sooner or later, resulting in dimming the lightbulb.
Here is a project that explains a project to make just that with an Arduino. http://www.instructables.com/id/Arduino-controlled-light-dimmer-The-circuit/step2/Arduino-controlled-light-dimmer-The-software/
Luckily this hardware is also readily built available, here is an example: http://www.inmojo.com/store/inmojo-market/item/digital-ac-dimmer-module/
You can control a solid-state relay with a microcontroller output. And if you need more current than that, the solid-state relay can control a bigger non-solid-state relay.
Be careful if you really don't know what you are doing, you can hurt or kill someone with 110 VAC.
Ya use a interfacing circuit between the low voltage circuit and high voltage circuit. Interfacing may contain an isolator and some transistor or darlington pair( if you want to increase current )