On the Wedderburn Principal Theorem in Conformal Algebras
نویسنده
چکیده
We investigate an analogue of the Wedderburn principal theorem for associative conformal algebras with finite faithful representations. It is shown that the radical splitting property for an algebra of this kind holds if the maximal semisimple factor of this algebra is unital, but does not hold in general.
منابع مشابه
On the Wedderburn Principal Theorem for Conformal Algebras
We investigate an analogue of the Wedderburn principal theorem for associative conformal algebras with finite faithful representations. It is shown that the radical splitting property for an algebra of this kind holds if the maximal semisimple factor of this algebra is unital, but does not hold in general.
متن کاملThe 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...
متن کاملComputing the Wedderburn decomposition of group algebras by the Brauer-Witt theorem
We present an alternative constructive proof of the Brauer–Witt theorem using the so-called strongly monomial characters that gives rise to an algorithm for computing the Wedderburn decomposition of semisimple group algebras of finite groups.
متن کاملAn extension of the Wedderburn-Artin Theorem
In this paper we give conditions under which a ring is isomorphic to a structural matrix ring over a division ring.
متن کاملAn algorithm to compute the Wedderburn decomposition of semisimple group algebras implemented in the GAP package wedderga
We present an algorithm to compute the Wedderburn decomposition of semisimple group algebras based on a computational approach of the Brauer-Witt theorem. The algorithm was implemented in the GAP package wedderga.
متن کامل