This is a very common question, and the short answer is: not really.
Here, alvorligt is best understood as part of the expression tage noget alvorligt = take something seriously.
A useful way to think about it:
- alvorlig = serious
- alvorligt = seriously / in a serious way
So in this sentence, alvorligt does not simply mean serious as an adjective directly describing arbejde. It describes how the speaker takes their work.
That is why the English translation uses seriously, not serious.
So although the -t form often looks like the neuter form of an adjective, here it is functioning more like an adverbial form in the expression.