间隔p Virasoro 代数的导子代数和自同构群

Derivation algebra and automorphism group of gap-p Virasoro algebras

Virasoro代数作为圆上的多项式向量场的复李代数的泛中心扩张在二维共形量子场论中起到奠基性作用,间隔p Virasoro代数是一类与无心的Heisenberg-Virasoro代数密切相关的无限维李代数.本文研究了间隔p Virasoro代数的导子代数和自同构群.特别地,本文给出间隔p Virasoro代数到它自身的一阶同调群和所有的外导子.

As the universal central extension of the complex Lie algebra of the linear operators over the circle,Virasoro algebra plays a key role in the 2-dimensional conformal field theory.Gap-p Virasoro algebras is a kind of infinite dimensional Lie algebras which related closely with the centerless Heisenberg-Virasoro algebra.In this paper,the authors determine their derivations and automorphism group.In particular,we compute the first cohomology group with their coefficients in themselves and all outer derivation.