Some Simple Subalgebras of Generalized Block Algebras

Abstract

Let A be an abelian group, let F be an arbitrary field of characteristic Ž . 0, let a g Hom A, F , and let w : A = A a F be a skew-symmetric Ž . biadditive map such that w s a n b holds for some b g Hom A, F . We note that such b is not unique since we can replace b with b q ca for Ž . any c g F. Then we can construct the Lie algebra L s L A, a , w by taking a vector space over F with a basis consisting of all symbols e , x x g A, and by defining the Lie algebra structure on this space by