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Jie-Tai Yu

  1. Isomorphisms between affine Hecke algebras.

    Tue, 01/12/2010 - 16:01 — SomNambul
    Authors: Jie-Tai Yu, Nan-Hua Xi
    Subjects: Quantum Algebra
    Abstract

    Let $k$ be a field and suppose $p, q\in k$. We prove that the two affine
    Hecke algebras $H_q$ and $H_p$ of type $A_n$ are isomorphic as $k$-algebras if
    and only if $p=q^{\pm 1}$.

  2. Isomorphisms between quantum groups $U_q(\mathfrak{sl}_{n+1})$ and $U_p(\mathfrak{sl}_{n+1})$.

    Tue, 01/05/2010 - 16:01 — SomNambul
    Authors: Li-Bin Li, Jie-Tai Yu
    Subjects: Rings and Algebras
    Abstract

    Let $\mathbb K$ be a field and suppose $p, q\in\mathbb K^*$ are not roots of
    unity. We prove that the two quantum groups $U_q(\mathfrak {sl}_{n+1})$ and
    $U_p(\mathfrak{sl}_{n+1})$ are isomorphic as $\mathbb K$-algebras implies that
    $p=\pm q^{\pm 1}$ when $n$ is even. This new result answers a classical
    question of Jimbo.

  3. Isomorphisms and automorphisms of quantum groups.

    Mon, 10/12/2009 - 10:31 — SomNambul
    Authors: Li-Bin Li, Jie-Tai Yu
    Subjects: Quantum Algebra
    Abstract

    We consider isomorphisms and automorphisms of quantum groups. Let $k$ be a
    field and suppose $p, q\in k^*$ are not roots of unity. We prove that the two
    quantum groups $U_q(\mathfrak {sl}_2)$ and $U_p(\mathfrak{sl}_2)$ over a field
    $k$ are isomorphic as $k$-algebras if and only if $p=q^{\pm 1}$. We also
    describe the group of all $k$-automorphisms of $U_q(\mathfrak{sl}_2)$ and prove
    that $\text{Aut}_k(U_q(\mathfrak {sl}_2))$ is isomorphic to
    $\text{Aut}_k(U_p(\mathfrak {sl}_2))$

  4. Isomorphisms and automorphisms of quantum groups.

    Mon, 10/12/2009 - 10:31 — SomNambul
    Authors: Li-Bin Li, Jie-Tai Yu
    Subjects: Quantum Algebra
    Abstract

    We consider isomorphisms and automorphisms of quantum groups. Let $k$ be a
    field and suppose $p, q\in k^*$ are not roots of unity. We prove that the two
    quantum groups $U_q(\mathfrak {sl}_2)$ and $U_p(\mathfrak{sl}_2)$ over a field
    $k$ are isomorphic as $k$-algebras if and only if $p=q^{\pm 1}$. We also
    describe the group of all $k$-automorphisms of $U_q(\mathfrak{sl}_2)$ and prove
    that $\text{Aut}_k(U_q(\mathfrak {sl}_2))$ is isomorphic to
    $\text{Aut}_k(U_p(\mathfrak {sl}_2))$

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