Article ال

Assalamu 3leikum
Why we don't use hamza with alif in article ال? 

Jazakum llahu khair.

Wa alaikum assalam,

I think you mean why we don't write the  ا  in  ال  as أل ( with hamzah above it)

Because that hamzah is hamzat wasl (hamzatul wasl means you don't pronounce the hamzah in continuous reading or talking.) and it is written as ا (without hamzah above it)

Hamzatul wasl: you don't pronounce it in continuous reading or talking (when the word is in the middle of a sentence), but you pronounce it when it is in the beginning of the sentence.

For example, قرأت الكتاب is written as: qara'tu al-kitaab. But you pronounce it as: qara'tul-kitaab.

as you can see the letter ا (a) is omtitted in pronunciation only.

However, when you begin reading or talking with ال you should pronounce the hamzah e.g. الكتاب is written as 'al-kitaab' and pronounced as 'al kitaab' 

ال التعريف 

لماذا لا نستخدم الهمزة مع ال التعريف؟

جزاكم الله خيرا

honestly, I do not know. I make a search on internet to figure out this problem and I found this site, I hope it help you

 http://www.oudnad.net/spip.php?article183