Structure of a Class of Lie Algebras of Block Type

摘要

Let b{script} (q) be a class of Lie algebras of Block type with basis {L _(α, i) {pipe} α, i ∈ ?, i ≥ 0} and relations [L _(α, i), L _(β, j)] = (β(i + q) - α(j + q))L _(α+β, i+j), where q is a positive integer. In this article, it is shown that b{script}(q) are different from each other for distinct positive integers q's. The automorphism groups, the derivation algebras, and the central extensions of all b{script}(q) are also uniformly and explicitly described, which generalize some previous results.