No abstract

Let A be a semiprime associative algebra with an involution ∗ over a field of characteristic not 2, let KA be the Lie algebra of all skew elements of A, and let ZKA denote the annihilator of KA. The aim of this paper is to prove that if Q is a ∗-subalgebra of Qs(A) (the Martindale symmetric algebra of quotients of A) containing A, then KQ/ZKQ is a Lie algebra of quotients of KA/ZKA. Similarly, [KQ, KQ]/Z[KQ,KQ] is a Lie algebra of quotients of [KA,KA]/Z[KA,KA].

No abstract

In this paper we explore graded algebras of quotients of Lie algebras with special emphasis on the 3-graded case and answer some natural questions concerning its relation to maximal Jordan systems of quotients.

The motivation for this paper is the study of the relation between the zero component of the maximal graded algebra of quotients and the maximal graded algebra of quotients of the zero component, both in the Lie case and when considering Martindale algebras of quotients in the associative setting. We apply our results to prove that the finitary complex Lie algebras are (graded) strongly nondegenerate and compute their maximal algebras of quotients.