arXiv subjects

Haifeng Lian

Publications and source records attributed to Haifeng Lian.

3 recordsLinked to original sources

arXiv2014

Whittaker modules for the derivation Lie algebra of torus with two variables

Let $\mathcal{L}$ be the derivation Lie algebra of ${\mathbb C}[t_1^{\pm 1},t_2^{\pm 1}]$. Given a triangle decomposition $\mathcal{L} =\mathcal{L}^{+}\oplus\mathfrak{h}\oplus\mathcal{L}^{-}$, we define a nonsingular Lie algebra homomorphism $ψ:\mathcal{L}^{+}\rightarrow\mathbb{C}$ and the universal Whittaker $\mathcal{L}$-module $W_ψ$ of type $ψ$. We obtain all Whittaker vectors and submodules of $W_ψ$, and all simple Whittaker $\mathcal{L}$-modules of type $ψ$.

math.RT↗

arXiv2012

N-derivations for finitely generated graded Lie algebras

$N$-derivation is the natural generalization of derivation and triple derivation. Let ${\cal L}$ be a finitely generated Lie algebra graded by a finite dimensional Cartan subalgebra. In this paper, a sufficient condition for Lie $N$-derivation algebra of ${\cal L}$ coinciding with Lie derivation algebra of ${\cal L}$ is given. As applications, any $N$-derivation of Schrödinger-Virasoro algebra, generalized Witt algebras, Kac-Moody algebras and their Borel subalgebras, is a derivation.

math.RA↗

arXiv2012

On permanents of matrices over a commutative additively idempotent semiring

Let $R$ be a commutative additively idempotent semiring. In this paper, some properties and characterizations for permanents of matrices over $R$ are established, and several inequalities for permanents are given. Also, the adjiont matrices of matriecs over $R$ are considered. Partial results obtained in this paper generalize the corresponding ones on fuzzy matrices, on lattice matrices and on incline matrices.

math.RA↗