* I - Pronoun (subject)
* have written - Verb (present perfect tense)
* a - Indefinite article (modifies "book")
* book - Noun (object)
There are no adverbs in this sentence. Adverbs modify verbs, adjectives, or other adverbs, and there's no word in the sentence describing how or when the writing was done.
The adjective in the sentence is "a". While it's technically an indefinite article, articles are a type of adjective because they modify nouns. In this case, "a" tells us that the speaker has written one book, not multiple.