The Ampeg 810E is rated at 4 ohms. You should be fine pushing this cab with a DG 500.
Older DG500s are rated to 2 ohms minimum. I just looked at the website and the specs on current DG500s appear to be 3 ohms minimum. This shows in the graphic of the back of the amps and also in the specs table of the manuals.
For all practical purpose this means the amp is now rated at 4 ohms minimum. For example one 4 ohm cab or a pair of 8 ohm cags will provide a 4 ohm nominal load.
I don't know if the amp has been updated or if DG simply derated the output section because the amps were havingt problems at 2 ohms. Before running your amp at 2 ohms, I suggest contacting DG.
The technical bits:
Tube amps use a transformer, so impedance matching is the goal. Many tube amps have multiple output taps, so you calculate the load of your speakers and connect them to an appropriate output tap. For example if you have a pair of 8 ohms cabs, they will provide a load or 4 ohms when connected in parallel. Use the 4 ohm output tap on the amp.
This can be confusing because of the way the outputs are labeled. For example, the speaker outs on an Orange AD200B look like this:
The output transformer in this amp has an 8 ohm tap and a 4 ohm tap. The 4 ohm tap is connected to two jacks that are in parallel.
You might assume that you can connect two 4 ohm cabs, but this is incorrect. That would result in a 2 ohm load, so it would be an impedance mismatch.
You can run one 8 ohm cab off the 8 ohm jack. Or you can run one 4 ohm cab off one of the 4 ohm jacks. Or you can run two 8 ohm cabs off the 4 ohm jacks. Or you can daisy chain a pair of 8 ohm cabs off one of the 4 ohm jacks.
Solid state amps are a bit different. In general, they try to make the same voltage regardless of the load. As the impedance of the load goes down, it allows more current to flow and the power goes up.
Current produces heat, and if you pull too much current from the amp it will cause the output section to overheat. Because of this, solid state amps have a minimum load spec. If you run a lower impedance than the amp is rated for, the amp may either go into protect mode or experience damage.
Some solid state amps have an impedance switch. For example the Mesa Subway 800W amps have a switch that is labeled like this:
This is also a little confusing as the intent is to use the 2 ohm setting if the impedance of the load drops below 4 ohms. For example if you run three 8 ohm cabs in parallel, the resulting load is 2.67ohms, so the switch should be set to the 2 ohm position.
This amp is rated for 400W at 8 ohms, 800W at 4 or 2 ohms. My understanding is the switch primarily reconfigures the power supply to lower the voltage sent to the output section. Lowering the voltage results in less current.
Impedance switches can work different in other solid state amp. For example in some instances the switch changes the limiter settings on the output model to keep the amp from exceeding power levels it can safely produce.
