Admissible groups, symmetric factor sets, and simple algebras

Admissible Groups , Symmetric Factor Sets , and Simple Algebras

Let K be a field of characteristic zero and suppose that D is a K-fv.lslpn algebra; i.e. a finite dimensional division algebra over K with center K. In Mollin [i] we proved that if K contains no non-trivial odd order roots of unity, then every finite odd order subgroup of D the multiplicative group of D, is cyclic. The first main result of this paper is to generalize (and simplify the proof of)...

Graded Algebras, Anti-involutions, Simple Groups and Symmetric Spaces

Asymptotic Results on Modular Representations of Symmetric Groups and Almost Simple Modular Group Algebras

In fact, this is a question about infinite simple groups because it is easy for G finite, and because a non-trivial normal subgroup gives rise to a non-trivial ideal different from the augmentation ideal. Also note that the problem reduces easily to the question on when the augmentation ideal is simple as a ring. The first interesting class of groups with almost simple FG was discovered in [3]....

Lie-admissible Algebras and Operads

A Lie-admissible algebra gives a Lie algebra by anticommutativity. In this work we describe remarkable types of Lie-admissible algebras such as Vinberg algebras, pre-Lie algebras or Lie algebras. We compute the corresponding binary quadratic operads and study their duality. Considering Lie algebras as Lie-admissible algebras, we can define for each Lie algebra a cohomology with values in an Lie...

Survey Article Simple Groups and Simple Lie Algebras

One of the main aims of workers in the theory of groups has always been the determination of all finite simple groups. For simple groups may be regarded as the fundamental building blocks out of which finite groups are constructed. The cyclic groups of prime order are trivial examples of simple groups, and are the only simple groups which are Abelian. The first examples of non-Abelian simple gr...