arXiv subjects
Publications and source records attributed to Zhixiang Wu.
We prove that any smooth irreducible supersingular representation with central character of $\text{GL}_2(F)$ is never of finite presentation when $F$ is a finite field extension of $\mathbb{Q}_p$ such that $F\neq \mathbb{Q}_p$, extending a result of Schraen for quadratic extensions.
We define a series of Artin-Schelter Gorenstein Hopf algebras $H_β$ with injective dimensions 3. Radford's Hopf algebra and Gelaki's Hopf algebra are homomorphic images of $H_β$. We determine its Grothendieck ring $G_0(H_β)$. Meanwhile we can obtain Grothendieck rings of Gelaki's Hopf algebras and Radford's Hopf algebras $U_{(N,ν,ω)}$ in \cite{R}, and non-isomorphic Hopf algebras with isomorphic Grothendieck rings.
Lie conformal algebras $\mathcal{W}(a,b)$ are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we give a complete classification of extensions of finite irreducible conformal modules of $\mathcal{W}(a,b)$. With a similar method, we characterize all extensions of finite irreducible conformal modules of Schrödinger-Virasoro type Lie conformal algebras $TSV(a,b)$ and $TSV(c)$.
Lie conformal algebras $\mathcal{W}(a,b)$ are the semi-direct sums of Virasoro Lie conformal algebra and its nontrivial conformal modules of rank one. In this paper, we first give a complete classification of all finite nontrivial irreducible conformal modules of $\mathcal{W}(a,b)$. It is shown that all such modules are of rank one. Moreover, with a similar method, all finite nontrivial irreducible conformal modules of Schrödinger-Virasoro type Lie conformal algebras $TSV(a,b)$ and $TSV(c)$ are characterized.
Schrodinger-Virasoro Lie algebras are annihilation algebras of Lie conformal algebras of rank three, which are widely studied by mathematicians and physicists. Conformal algebras are also called H-pseudoalgebras, where H = k[s] is the polynomial algebra over a field k. In this article, we introduce and classify Schrodinger-Virasoro Lie H-pseudoalgebras. Meanwhile we also determine all Leibniz H-pseudoalgebras of rank two.
In this paper, simplicity of quadratic Lie conformal algebras are investigated. From the point view of the corresponding Gel'fand-Dorfman bialgebras, some sufficient conditions and necessary conditions to ensure simplicity of quadratic Lie conformal algebras are presented. By these observations, we present several classes of new infinite simple Lie conformal algebras. These results will be useful for classification purposes.
In this paper we describe certain homological properties and representations of a two-parameter quantum enveloping algebra $U_{g,h}$ of ${\frak {sl}}(2)$, where $g,h$ are group-like elements.
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