Invariant Wedderburn factors

Wedderburn Polynomials over Division Rings

A Wedderburn polynomial over a division ring K is a minimal polynomial of an algebraic subset of K. Special cases of such polynomials include, for instance, the minimal polynomials (over the center F = Z(K)) of elements of K that are algebraic over F . In this note, we give a survey on some of our ongoing work on the structure theory of Wedderburn polynomials. Throughout the note, we work in th...

Wedderburn decomposition of finite group algebras

We show a method to effectively compute the Wedderburn decomposition and the primitive central idempotents of a semisimple finite group algebra of an abelian-by-supersolvable group G from certain pairs of subgroups of G. In this paper F = Fq denotes a finite field with q elements and G is a finite group of order n such that FG is semisimple, or equivalently (q, n) = 1. The group algebra FG is a...

The Wedderburn Principal Theorem for Alternative Algebras

for all a, x in 21. I t is clear that associative algebras are alternative. The most famous examples of alternative algebras which are not associative are the so-called Cayley-Dickson algebras of order 8 over $. Let S be an algebra of order 2 over % which is either a separable quadratic field over 5 or the direct sum 5 ©3There is one automorphism z—>z of S (over %) which is not the identity aut...

An Introduction to Wedderburn Theory & Group Representations

Semisimple Synchronizing Automata and the Wedderburn-Artin Theory