The forward voltage of a LED is a (more or less, depends on current) fixed value so the resistor does not lower the voltage. You need to limit the current through the LED and that is what the resistor is for.
You need a higher voltage than the 11V to be able to limit the current; e.g. 15V. See below image
You now need to calculate the values for the resistor.

Value.
If you want the 1A current (max brightness), the V_{f} is actually 12 V (and not 11 V, see first graph on page 18 of the datasheet ) and there will be 15V  12V over the resistor. So according to Ohm's law (V = I * R
), R will be 3 Ohm.

Power.
The power dissipated in the resistor is the voltage over the resistor multiplied by the current through the resistor so is 3 W; you will have to pick a resistor that at least has that power rating (the ones that come with e.g. kits are either 1/8 or 1/4 Watt and not suitable).
If you want to limit the current to approx. 200 mA, V_{f} is about 11 V. So the calculation will result in 4 / 0.2 = 20 Ohm and the ower dissibation will be 4 * 0.2 = 0.8 W (rounded 1W).
Take the worse case scenario (3 W) !!
If you power with 13 V instead of 15 V, you're better of as the numbers for e.g. 1 A result in 1 V over the resistor (so 1 Ohm) and 1 Watt.
Lastly, you can not drive this directly from an Arduino; you will need a logic level Nchannel mosfet between the LED and the GND.