2015/12/03 by Barry, Demba
#11E39 #16W60 #16W70 #FOS: Mathematics #Primary 16W10 #Rings and Algebras (math.RA) #Secondary 16K20
paper · doi:10.48550/arxiv.1512.01083
We study possible decompositions of totally decomposable algebras with involution, that is, tensor products of quaternion algebras with involution. In particular, we are interested in decompositions in which one or several factors are the split quaternion algebra M2(F), endowed with an orthogonal involution. Using the theory of gauges, developed by Tignol-Wadsworth, we construct examples of algebras isomorphic to a tensor product of quaternion algebras with k split factors, endowed with an involution which is totally decomposable, but does not admit any decomposition with k factors M2(F) with involution. This extends an earlier result of Sivatski where the algebra considered is of degree 8 and index 4, and endowed with some orthogonal involution.