Structure of the Lie Algebras Related to Those of Block

Abstract

We determine the isomorphism classes of the first family of infinite dimensional simple Lie algebras recently introduced by Xu. The structure space of these algebras is given explicitly. The derivations of these algebras are also determined.

Representations of the Quantized Weyl Algebra Associated to the Quantum Plane

“…The Virasoro-like algebra is closely related to the Lie algebras of Block type [10,17,19] and the generalized Virasoro algebras [14], as can be seen from the structure theory of these Lie algebras [7,10,16,17]. The representation theory of these related Lie algebras has been an interesting object in recent years (see, for example, [6,9,11,12,14,18]).…”

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]).…”

Weight modules over some Block algebras

“…Generalizations of Block algebras have been studied by many authors (see, for example, [2][3][4][5][6][7]). Partially because they are closely related to the Virasoro algebra, these algebras have attracted some attention in the literature.…”