Title:  The Word Problem for the Brauer Group

 

Abstract:  By the renown Merkurjev-Suslin Theorem, the Brauer group of a field is generated by symbol algebras.  This gives rise to the word problem - given two ``words" (i.e. tensor products of symbol algebras), one should like to determine whether they represent the same element in the group or not.  One way to approach this problem is to come up with a way of producing all the equivalent words to one given word.  We shall discuss the special case of quaternion algebras and present some new results.