Structures of Generalized Loop Virasoro Algebras

Abstract

In this article, we study the structure theory of a class of generalized loop Virasoro algebras. In particular, the derivation algebras, the automorphism groups, and the second cohomology groups of generalized loop centerless Virasoro algebras are determined.

Structures of Not-finitely Graded Lie Algebras Related to Generalized Virasoro Algebras

“…for α ∈ Γ and some τ ∈ χ(Γ), c ∈ Γ C * (e.g., [11]), this result can also be proved directly by noting that C * L 0,0 is the set of nonzero ad-locally finite elements in Vir(Γ)). By replacing σ by σφ…”

“…Various generalizations of the Virasoro algebra have been studied by several authors (e.g., [3][4][5][8][9][10][11][12]). In this paper, (1+t) i , a ∈ Γ, i ∈ Z + .…”

“…One must employ some new techniques in order to tackle problems associated with not-finitely graded and not-finitely generated Lie algebras (this is also one of our motivations to present our results here). For instance, one of our strategies used in the present paper is to embed W into its completed algebra W (see (3.3)) so that the determination of derivations can be done much more efficiently than that in some classical methods in the literature (e.g., [11] …”

Structures of generalized loop super-Virasoro algebras

“…The loop Virasoro algebra is the Lie algebra of the tensor product of the Virasoro algebra and the Laurent polynomial algebra. The irreducible Harish-Chandra modules over loop Virasoro algebra were classified in [8]; while the structure of the generalized loop Virasoro algebra W L [Γ] was considered in [26]. Motivated by these, we consider the following Lie superalgebra …”

Structures of not-finitely graded Lie algebras related to generalized Heisenberg–Virasoro algebras

“…In recent years, some researches on Lie algebras concerning their derivation algebras, automorphisms, second cohomology groups have been undertaken by many authors (see, e.g., [3][4][5][11][12][13][14][15][16][17]). It is well known that central extensions, which are determined by second cohomology groups, are closely related to the structures of Lie algebras (see, e.g., [6,7]).…”