Yao-Z Zhang

activity

19922023

most citedDimerization in a half-filled one-dimensional extended Hubbard model

95 citations · 2.4k across the 176 of their papers we have counts for

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Showing math.QAShow all

25 papers · 1 filter

math.QA2017★ 1 cited

Structures of Nichols (braided) Lie algebras of diagonal type

Weicai Wu, Jing Wang, Shouchuan Zhang +1

Let $V$ be a braided vector space of diagonal type. Let $B (V)$ , $L^{-} (V)$ and $L (V)$ be the Nichols algebra, Nichols Lie algebra and Nichols braided Li…

math.QA2016★ 3 cited

Finiteness of Nichols Algebras and Nichols (Braided) Lie Algebras

Weicai Wu, Shouchuan Zhang, Yao-Zhong Zhang

It is shown that if $B (V)$ is connected Nichols algebra of diagonal type with $dim V > 1$ , then $dim (L^{-} (V)) = \infty$ $($ resp. $ \dim (\mathfrak L(V)) = \inf…

math.QA2014★ 4 cited

On Nichols (braided) Lie algebras

Weicai Wu, Shouchuan Zhang, Yao-Zhong Zhang

We prove {\rm (i)} Nichols algebra $B (V)$ of vector space $V$ is finite-dimensional if and only if Nichols braided Lie algebra $L (V)$ is finite-dimensional; {\r…

math.QA2014★ 1 cited

Relationship between Nichols braided Lie algebras and Nichols algebras

Weicai Wu, Shouchuan Zhang, Yao-Zhong Zhang

We establish the relationship among Nichols algebras, Nichols braided Lie algebras and Nichols Lie algebras. We prove two results: (i) Nichols algebra $B (V)$ is finite-di…

math.QA2013

Nichols algebras over classical Weyl groups, Fomin-Kirillov algebras and Lyndon basis

Shouchuan Zhang, Weicai Wu, Zhengtang Tan +1

We show that except in several cases conjugacy classes of classical Weyl groups $W (B_{n})$ and $W (D_{n})$ are of type {\rm D}. We prove that except in three cases Nichols algebras of i…

math.QA2009★ 3 cited

Pointed Hopf Algebras with classical Weyl Groups

Shouchuan Zhang, Yao-Zhong Zhang

We prove that Nichols algebras of irreducible Yetter-Drinfeld modules over classical Weyl groups $A ⋊ S_{n}$ supported by $S_{n}$ are infinite dimensional, except…

math.QA2008★ 9 cited

On Pointed Hopf Algebras with Weyl Groups of exceptional type

Shouchuan Zhang, Yao-Zhong Zhang, Peng Wang +2

All -1-type pointed Hopf algebras and central quantum linear spaces with Weyl groups of exceptional type are found. It is proved that every non -1-type pointed Hopf algebra with re…

math.QA2008★ 7 cited

Classification of Quiver Hopf Algebras and Pointed Hopf Algebras of Type One

Shouchuan Zhang, Hui-Xiang Chen, Yao-Zhong Zhang

The quiver Hopf algebras are classified by means of ramification systems with irreducible representations. This leads to the classification of Nichols algebras over group algebras…

math.QA2006★ 7 cited

Local Quasitriangular Hopf Algebras

Shouchuan Zhang, Mark D. Gould, Yao-Zhong Zhang

We find a new class of Hopf algebras, local quasitriangular Hopf algebras, which generalize quasitriangular Hopf algebras. Using these Hopf algebras, we obtain solutions of the Yan…

math.QA2004

Classification of PM Quiver Hopf Algebras

Shouchuan Zhang, Yao-Zhong Zhang, Hui-Xiang Chen

We describe certain quiver Hopf algebras by parameters. This leads to the classification of multiple Taft algebras as well as pointed Yetter-Drinfeld modules and their correspondin…

math.QA2004★ 5 cited

Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras

Fang Li, Yao-Zhong Zhang

The concept of biperfect (noncocommutative) weak Hopf algebras is introduced and their properties are discussed. A new type of quasi-bicrossed products are constructed by means of…

math.QA2004★ 21 cited

A Unified and Complete Construction of All Finite Dimensional Irreducible Representations of gl(2|2)

Yao-Zhong Zhang, Mark D. Gould

Representations of the non-semisimple superalgebra $g l (2∣2)$ in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All…

math.QA2000★ 6 cited

Level-one Highest Weight Representation of $U_{q} [s l (N ∣1)^]$ and Bosonization of the Multi-component Super t-J Model

Wen-Li Yang, Yao-Zhong Zhang

We study the level-one irreducible highest weight representations of the quantum affine superalgebra $U_{q} [s l (N ∣1)^]$ , and calculate their characters and supercharacters. We ob…

math.QA1999★ 4 cited

$U_{q} [s l (2∣1)^]$ Vertex Operators, Screen Currents and Correlation Functions at Arbitrary Level

Yao-Zhong Zhang, Mark D. Gould

Bosonized q-vertex operators related to the 4-dimensional evaluation modules of the quantum affine superalgebra $U_{q} [s l (2∣1)^]$ are constructed for arbitrary level $k = α$ , wher…

math.QA1999★ 7 cited

Vertex Operators of $U_{q} [g l (N ∣ N)^]$ and Highest Weight Representations of $U_{q} [g l (2∣2)^]$

Wen-Li Yang, Yao-Zhong Zhang

We determine the exchange relations of the level-one q-vertex operators of the quantum affine superalgebra $U_{q} [g l (N ∣ N)^]$ . We study in details the level-one irreducible highe…

math.QA1999★ 5 cited

Level-One Highest Weight Representations of $U_{q} [g l (1∣1)^]$ and Associated Vertex Operators

Wen-Li Yang, Yao-Zhong Zhang

We study the level-one irreducible highest weight representations of $U_{q} [g l (1∣1)^]$ and associated q-vertex operators. We obtain the exchange relations satisfied by the verte…

math.QA1999★ 13 cited

Twisted Quantum Affine Superalgebra $U_{q} [g l (m ∣ n)^{(2)}]$ and New $U_{q} [os p (m ∣ n)]$ Invariant R-matrices

Mark D. Gould, Yao-Zhong Zhang

The minimal irreducible representations of $U_{q} [g l (m ∣ n)]$ , i.e. those irreducible representations that are also irreducible under $U_{q} [os p (m ∣ n)]$ are investigated and shown to be a…

math.QA1999★ 23 cited

Twisting invariance of link polynomials derived from ribbon quasi-Hopf algebras

J. R. Links, M. D. Gould, Y. -Z. Zhang

The construction of link polynomials associated with finite dimensional representations of ribbon quasi-Hopf algebras is discussed in terms of the formulation of an appropriate Mar…

math.QA1999★ 20 cited

The twisted quantum affine algebra $U_q(A^{(2)_2)$ and correlation functions of the Izergin-Korepin model

Bo-yu Hou, Wen-Li Yang, Yao-Zhong Zhang

We derive the exchange relations of the vertex operators of $U_{q} (A_{2}^{(2)})$ and show that these vertex operators give the bosonization of the Izergin-Korepin model. We give an int…

math.QA1999★ 8 cited

Drinfeld Basis And a Nonclassical Free Boson Representation of Twisted Quantum Affine Superalgebra $U_{q} [os p (2∣2)^{(2)}]$ }

Wen-Li Yang, Yao-Zhong Zhang

We derive from the super RS algebra the Drinfeld basis of the twisted quantum affine superalgebra $U_{q} [os p (2∣2)^{(2)}]$ by means of the Gauss decomposition technique. We explicitly…

math.QA1998★ 16 cited

Highest weight representations of $U_{q} (s l^(2∣1))$ and correlation functions of the q-deformed supersymmetric t-J model

Wen-Li Yang, Yao-Zhong Zhang

We re-examine the level-one irreducible highest weight representations of the quantum affine superalgebra $U_{q} (s l^(2∣1))$ and derive the characters and supercharacters associa…

math.QA1998★ 16 cited

Level-One Representations and Vertex Operators of Quantum Affine Superalgebra $U_{q} [g l (N ∣ N)^]$

Yao-Zhong Zhang

Level-one representations of the quantum affine superalgebra $U_{q} [g l (N ∣ N)^]$ associated to the appropriate non-standard system of simple roots and $q$ -vertex operators (intert…

math.QA1998

On Quasi-Hopf superalgebras

Mark D. Gould, Yao-Zhong Zhang, Phillip S. Isaac

In this work we investigate several important aspects of the structure theory of the recently introduced quasi-Hopf superalgebras (QHSAs), which play a fundamental role in knot the…

math.QA1998★ 24 cited

Casimir Invariants from Quasi-Hopf (Super)algebras

Mark. D. Gould, Yao-Zhong Zhang, Phillip S. Isaac

We show how to construct, starting from a quasi-Hopf (super)algebra, central elements or Casimir invariants. We show that these central elements are invariant under quasi-Hopf twis…

Structures of Nichols (braided) Lie algebras of diagonal type

Finiteness of Nichols Algebras and Nichols (Braided) Lie Algebras

On Nichols (braided) Lie algebras

Relationship between Nichols braided Lie algebras and Nichols algebras

Nichols algebras over classical Weyl groups, Fomin-Kirillov algebras and Lyndon basis

Pointed Hopf Algebras with classical Weyl Groups

On Pointed Hopf Algebras with Weyl Groups of exceptional type

Classification of Quiver Hopf Algebras and Pointed Hopf Algebras of Type One

Local Quasitriangular Hopf Algebras

Classification of PM Quiver Hopf Algebras

Quantum Doubles from a Class of Noncocommutative Weak Hopf Algebras

A Unified and Complete Construction of All Finite Dimensional Irreducible Representations of gl(2|2)

Level-one Highest Weight Representation of Uq​[sl(N∣1)^​] and Bosonization of the Multi-component Super t-J Model

Uq​[sl(2∣1)^​] Vertex Operators, Screen Currents and Correlation Functions at Arbitrary Level

Vertex Operators of Uq​[gl(N∣N)^​] and Highest Weight Representations of Uq​[gl(2∣2)^​]

Level-One Highest Weight Representations of Uq​[gl(1∣1)^​] and Associated Vertex Operators

Twisted Quantum Affine Superalgebra Uq​[gl(m∣n)(2)] and New Uq​[osp(m∣n)] Invariant R-matrices

Twisting invariance of link polynomials derived from ribbon quasi-Hopf algebras

The twisted quantum affine algebra $U_q(A^{(2)_2)$ and correlation functions of the Izergin-Korepin model

Drinfeld Basis And a Nonclassical Free Boson Representation of Twisted Quantum Affine Superalgebra Uq​[osp(2∣2)(2)]}

Highest weight representations of Uq​(sl^(2∣1)) and correlation functions of the q-deformed supersymmetric t-J model

Level-One Representations and Vertex Operators of Quantum Affine Superalgebra Uq​[gl(N∣N)^​]

On Quasi-Hopf superalgebras

Casimir Invariants from Quasi-Hopf (Super)algebras

Level-one Highest Weight Representation of $U_{q} [s l (N ∣1)^]$ and Bosonization of the Multi-component Super t-J Model

$U_{q} [s l (2∣1)^]$ Vertex Operators, Screen Currents and Correlation Functions at Arbitrary Level

Vertex Operators of $U_{q} [g l (N ∣ N)^]$ and Highest Weight Representations of $U_{q} [g l (2∣2)^]$

Level-One Highest Weight Representations of $U_{q} [g l (1∣1)^]$ and Associated Vertex Operators

Twisted Quantum Affine Superalgebra $U_{q} [g l (m ∣ n)^{(2)}]$ and New $U_{q} [os p (m ∣ n)]$ Invariant R-matrices

Drinfeld Basis And a Nonclassical Free Boson Representation of Twisted Quantum Affine Superalgebra $U_{q} [os p (2∣2)^{(2)}]$ }

Highest weight representations of $U_{q} (s l^(2∣1))$ and correlation functions of the q-deformed supersymmetric t-J model

Level-One Representations and Vertex Operators of Quantum Affine Superalgebra $U_{q} [g l (N ∣ N)^]$