Kaiming Zhao

Representations of the virasoro-like algebra and its q-Analog

In this paper, some irreducible graded modules with 1-dimensional homogeneous spaces over the Virasoro-like algebra and its q-analogs are constructed. The unitarizability of these modules, and the conditions under which two of such irreducible graded modules are ismorphic are determined. Some other kinds of irreducible graded modules with 1-dimensional homogeneous spaces over the Virasorolike algebra and its q-analogs are also given.

Generalized Poisson brackets and lie algebras of type H in characteristic 0

Abstract. The Lie algebra of Cartan type H which occurs as a subalgebra of the Lie algebra of derivations of the polynomial algebra

Generalized cartan type k lie algebras in characteristic 0

F[x_1,\dots,x_n, x_{-1},\dots,x_{-n}]

Infinite Dimensional Lie Algebras of Type L

was generalized by the first author to a class which included a subalgebra of the derivations of the Laurent polynomials

Z × Z-GRADED LIE ALGEBRAS CONTAINING A VIRASORO ALGEBRA AND A HEISENBERG ALGEBRA

F[x_1,\dots,x_n,x_{-1}, \dots,x_{-n}, x_1^{-1},\dots,x_n^{-1},x_{-1}^{-1},\dots,x_{-n}^{-1}]

Weight sets of irreducible integrable representations of kac-moody algebras of indefinite type

. We show in this paper that these generalizations of Cartan type H algebras are isomorphic to certain generalizations of the classical algebra of Poisson brackets, and that it can be generalized further. In turn, these algebras can be recast in a form that is an adaption of a class of Lie algebras of characteristic p that was defined in 1958 be R. Block. A further generalization of these algebras is the main topic of this paper. We show when these algebras are simple, find their derivations, and determine all possible isomorphisms between two of these algebras.

Indexes of the weyl groups in the orthogonal groups of some kac-moody algebras

The Lie algebra of Cartan type K which occurs as a subalgebra of the Lie algebra of derivations of the polynomial algebra F[x0, x1,…, xn,xn−1,…,x−n], where F is a field of characteristic 0, was generalized by the first author to a class which included a subalgebra of the derivations of the Laurent polynomials F[x0,x1,…, xn,x−1,…,x−n,X0 −1x1 -1,…,xn −1,…,x−1 −1…,x−n −1]A further generalization of these algebras is the main topic of this paper. We show when these algebras are simple, determine all possible

Centers of Down–Up Algebras☆

Abstract In this paper, a class of infinite dimensional Lie algebras L(A, δ, α) over a field of characteristic 0 are studied. These Lie algebras, which we call here Lie algebras of type L, arose as one subclass in the recent classification of generalized Block algebras. We exhibit a large subclass of these algebras which are simple, as well as another subclass of these algebras which are never simple. For n > 1, simple Lie algebras of type L do not occur in any other known class of simple Lie algebras. In particular, for n > 1, these algebras have no toral elements. Simplicity in these algebras is equivalent to simplicity of an appropriate subalgebra. The notion of transitive ideal plays an important role in this theory.

Doubly Z-Graded Lie Algebras Containing a Virasoro Algebra☆

Let Z be the ring of integers. In this paper we classify Z × Z-graded Lie algebras A = i, j∈Z A i, j over a characteristic 0 field F with dim A i, j ≤ 1 for each i and j, satisfying the following three properties: I. A 0 = i∈Z A i, 0 ≃ Vir, the centerless Virasoro algebra; II. A 0,−1, A 0,0, A 0,1 span a Heisenberg algebra; III. A is generated by the centerless Virasoro algebra and the Heisenberg algebra.

A Characterization of the Block Lie Algebra and Itsq-Forms in Characteristic 0☆

In this paper, the weight sets of some irreducible and integrable representations, which are not highest or lowest weight representations, of rank two Kac-Moody algebras of indefinite type are completely determined.