S. Pumplün

ON THE ZEROS OF POLYNOMIALS OVER QUATERNIONS

ABSTRACT We review and expand some results on the number of zeros of polynomials over Hamiltons quaternions, with particular emphasis on those polynomials with coefficients in a degree two subfield.

Space-time block codes from nonassociative division algebras

Associative division algebras are a rich source of fully diverse space-time block codes (STBCs). In this paper the systematic construction of fully diverse STBCs from nonassociative algebras is discussed. As examples, families of fully diverse

Nonassociative quaternion algebras over rings

2\times 2

Sums of squares in octonion algebras

,

The nonassociative algebras used to build fast-decodable space-time block codes

2\times 4

How to obtain division algebras used for fast-decodable space-time block codes

multiblock and

Albert algebras over curves of genus zero and one

4\times 4

Fast-decodable MIDO codes from non-associative algebras

STBCs are designed, employing nonassociative quaternion division algebras.

Jordan Algebras Over Algebraic Varieties

Non-split nonassociative quaternion algebras over fields were first discovered over the real numbers independently by Dickson and Albert. They were later classified over arbitrary fields by Waterhouse. These algebras naturally appeared as the most interesting case in the classification of the four-dimensional nonassociative algebras which contain a separable field extension of the base field in their nucleus. We investigate algebras of constant rank 4 over an arbitrary ringR which contain a quadratic étale subalgebraS overR in their nucleus. A generalized Cayley-Dickson doubling process is introduced to construct a special class of these algebras.

Some Classes of Multiplicative Forms of Higher Degree

Sums of squares in composition algebras are investigated using methods from the theory of quadratic forms. For any integer m > 1 octonion algebras of level 2 m and of level 2 m + 1 are constructed.