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yohei ohta
yohei ohta
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$\newcommand{\dmod}{\text{-}\mathrm{mod}}$Let $A$ be a finite-dimensional quasi-Hopf algebra over a field $k$ and $A\dmod$ be the category of finite dimensional left $A$-modules. Since $A\dmod$ is a rigid monoidal category, its Drinfel’d center $\mathcal{Z}(A\dmod)$ is a rigid braided monoidal category. So we obtain quasi triangular quasi hopf-Hopf algebra $D(A)$ from $\mathcal{Z}(A\dmod)$ by using tannaka duality.

Question 1:Is there a (categorical) definition of Heisenberg double $H(A)$ for quasi hopf-Hopf algebra $A$?

Question 2: If the answer to the above question is yes,is $D(A)$ a subalgebra of $H(A)\otimes H(A)^{\mathrm{op}}$?

$\newcommand{\dmod}{\text{-}\mathrm{mod}}$Let $A$ be a finite-dimensional quasi-Hopf algebra over a field $k$ and $A\dmod$ be the category of finite dimensional left $A$-modules. Since $A\dmod$ is a rigid monoidal category, its Drinfel’d center $\mathcal{Z}(A\dmod)$ is a rigid braided monoidal category. So we obtain quasi triangular quasi hopf algebra $D(A)$ from $\mathcal{Z}(A\dmod)$ by using tannaka duality.

Question 1:Is there a (categorical) definition of Heisenberg double $H(A)$ for quasi hopf algebra $A$?

Question 2: If the answer to the above question is yes,is $D(A)$ a subalgebra of $H(A)\otimes H(A)^{\mathrm{op}}$?

$\newcommand{\dmod}{\text{-}\mathrm{mod}}$Let $A$ be a finite-dimensional quasi-Hopf algebra over a field $k$ and $A\dmod$ be the category of finite dimensional left $A$-modules. Since $A\dmod$ is a rigid monoidal category, its Drinfel’d center $\mathcal{Z}(A\dmod)$ is a rigid braided monoidal category. So we obtain quasi triangular quasi-Hopf algebra $D(A)$ from $\mathcal{Z}(A\dmod)$ by using tannaka duality.

Question 1:Is there a (categorical) definition of Heisenberg double $H(A)$ for quasi-Hopf algebra $A$?

Question 2: If the answer to the above question is yes,is $D(A)$ a subalgebra of $H(A)\otimes H(A)^{\mathrm{op}}$?

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YCor
YCor
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Is there a definition of Heisenberg double for quasi hopf-Hopf algebras?

Let$\newcommand{\dmod}{\text{-}\mathrm{mod}}$Let $A$ be a finite-dimensional quasi-Hopf algebra over a field $k$ and $A\text{-}mod$$A\dmod$ be the category of finite dimensional left $A$-modules. Since $A\text{-}mod$$A\dmod$ is a rigid monoidal category, its Drinfel’d center $\mathcal{Z}(A\text{-}mod)$$\mathcal{Z}(A\dmod)$ is a rigid braided monoidal category. So we obtain quasi triangular quasi hopf algebra $D(A)$ from $\mathcal{Z}(A\text{-}mod)$$\mathcal{Z}(A\dmod)$ by using tannaka duality.

Question 1:Is there a (categorical) definition of Heisenberg double $H(A)$ for quasi hopf algebra $A$?

Question 2: If the answer to the above question is yes,is $D(A)$ a subalgebra of $H(A)\otimes H(A)^{op}$$H(A)\otimes H(A)^{\mathrm{op}}$?

Is there a definition of Heisenberg double for quasi hopf algebras?

Let $A$ be a finite-dimensional quasi-Hopf algebra over a field $k$ and $A\text{-}mod$ be the category of finite dimensional left $A$-modules. Since $A\text{-}mod$ is a rigid monoidal category, its Drinfel’d center $\mathcal{Z}(A\text{-}mod)$ is a rigid braided monoidal category. So we obtain quasi triangular quasi hopf algebra $D(A)$ from $\mathcal{Z}(A\text{-}mod)$ by using tannaka duality.

Question 1:Is there a (categorical) definition of Heisenberg double $H(A)$ for quasi hopf algebra $A$?

Question 2: If the answer to the above question is yes,is $D(A)$ a subalgebra of $H(A)\otimes H(A)^{op}$?

Is there a definition of Heisenberg double for quasi-Hopf algebras?

$\newcommand{\dmod}{\text{-}\mathrm{mod}}$Let $A$ be a finite-dimensional quasi-Hopf algebra over a field $k$ and $A\dmod$ be the category of finite dimensional left $A$-modules. Since $A\dmod$ is a rigid monoidal category, its Drinfel’d center $\mathcal{Z}(A\dmod)$ is a rigid braided monoidal category. So we obtain quasi triangular quasi hopf algebra $D(A)$ from $\mathcal{Z}(A\dmod)$ by using tannaka duality.

Question 1:Is there a (categorical) definition of Heisenberg double $H(A)$ for quasi hopf algebra $A$?

Question 2: If the answer to the above question is yes,is $D(A)$ a subalgebra of $H(A)\otimes H(A)^{\mathrm{op}}$?

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yohei ohta
yohei ohta
  • 255
  • 1
  • 7

Is there a definition of Heisenberg double for quasi hopf algebras?

Let $A$ be a finite-dimensional quasi-Hopf algebra over a field $k$ and $A\text{-}mod$ be the category of finite dimensional left $A$-modules. Since $A\text{-}mod$ is a rigid monoidal category, its Drinfel’d center $\mathcal{Z}(A\text{-}mod)$ is a rigid braided monoidal category. So we obtain quasi triangular quasi hopf algebra $D(A)$ from $\mathcal{Z}(A\text{-}mod)$ by using tannaka duality.

Question 1:Is there a (categorical) definition of Heisenberg double $H(A)$ for quasi hopf algebra $A$?

Question 2: If the answer to the above question is yes,is $D(A)$ a subalgebra of $H(A)\otimes H(A)^{op}$?