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We fix the standard inner products on $\mathbb{C}^n$ and $\mathbb{C}^n\otimes \mathbb{C}^n$.

Is there an anlgebra structure on $\mathbb{C}^n$ with multiplication $m$ such that the adjoint operator $m^*: \mathbb{C}^n \to \mathbb{C}^n \otimes \mathbb{C}^n$ is a coproduct(Coalgebraic operation)?

Is there a bialgebra structure whose product and coproduct are adjoint of each other? Is there a Hopf algebra with the later property and the additional condition that the antipod map is an isometry?

Note: Note that the adjoint operatores are taken associated to the corresponding inner products

We fix the standard inner products on $\mathbb{C}^n$ and $\mathbb{C}^n\otimes \mathbb{C}^n$.

Is there an algebra structure on $\mathbb{C}^n$ with multiplication $m$ such that the adjoint operator $m^*: \mathbb{C}^n \to \mathbb{C}^n \otimes \mathbb{C}^n$ is a coproduct  (coalgebraic operation)?

Is there a bialgebra structure whose product and coproduct are adjoints of each other? Is there a Hopf algebra with the latter property, and the additional condition that the antipode map is an isometry?

Note: The adjoint operators are taken with respect to the corresponding inner products.

We fix the standard inner products on $\mathbb{C}^n$ and $\mathbb{C}^n\otimes \mathbb{C}^n$.

Is there an anlgebra structure on $\mathbb{C}^n$ with multiplication $m$ such that the adjoint operator $m^*: \mathbb{C}^n \otimes \mathbb{C}^n\to \mathbb{C}^n$ is a coproduct(Coalgebraic operation)?

Is there a bialgebra structure whose product and coproduct are adjoint of each other? Is there a Hopf algebra with the later property and the additional condition that the antipod map is an isometry?

Note: Note that the adjoint operatores are taken associated to the corresponding inner products

We fix the standard inner products on $\mathbb{C}^n$ and $\mathbb{C}^n\otimes \mathbb{C}^n$.

Is there an anlgebra structure on $\mathbb{C}^n$ with multiplication $m$ such that the adjoint operator $m^*: \mathbb{C}^n \to \mathbb{C}^n \otimes \mathbb{C}^n$ is a coproduct(Coalgebraic operation)?

Is there a bialgebra structure whose product and coproduct are adjoint of each other? Is there a Hopf algebra with the later property and the additional condition that the antipod map is an isometry?

Note: Note that the adjoint operatores are taken associated to the corresponding inner products

We fix the standard inner products on $\mathbb{C}^n$ and $\mathbb{C}^n\otimes \mathbb{C}^n$.

Is there an anlgebra structure on $\mathbb{C}^n$ with multiplication $m$ such that the adjoint operator $m^*: \mathbb{C}^n \otimes \mathbb{C}^n\to \mathbb{C}^n$ is a coproduct(Coalgebraic operation)?

Is there a bialgebra structure whose product and coproduct are adjoint of each other? Is there a hopf alfebra with the later property and the additional condition that the antipod map is an isometry?

Note: Note that the adjoint operatores are taken associated to the corresponding inner products

We fix the standard inner products on $\mathbb{C}^n$ and $\mathbb{C}^n\otimes \mathbb{C}^n$.

Is there an anlgebra structure on $\mathbb{C}^n$ with multiplication $m$ such that the adjoint operator $m^*: \mathbb{C}^n \otimes \mathbb{C}^n\to \mathbb{C}^n$ is a coproduct(Coalgebraic operation)?

Is there a bialgebra structure whose product and coproduct are adjoint of each other? Is there a Hopf algebra with the later property and the additional condition that the antipod map is an isometry?

Note: Note that the adjoint operatores are taken associated to the corresponding inner products