Algebras generated by two quadratic elements

Details Algebras generated by two quadratic elements Algebras generated by two quadratic elements

2009-11-28

arxiv.org/abs/0911.5431v1

Mathematics

Rings and Algebras

Scientific paper

Let K be a field of any characteristic and let R be an algebra generated by two elements satisfying quadratic equations. Then R is a homomorphic image of F=K for suitable a,b,c,d in K. We establish that F can be embedded into the 2x2 matrix algebra M_2(E[t]) with entries from the polynomial algebra E[t] over the algebraic closure E of K and that F and M_2(E) satisfy the same polynomial identities as K-algebras. When the quadratic equations have double zeros, our result is a partial case of more general results by Ufnarovskij, Borisenko and Belov from the 1980's. When each of the equations has different zeros, we improve a result of Weiss, also from the 1980's.

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