All Questions
5 questions
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How to make sense of $\mathrm{Mat}_q(n \times n)$? Are there notions of quantum vector space, quantum linear algebra, etc?
Given some algebra $\mathcal{A}$ and $q \in \mathbb{C}$, we say that a matrix $M \in \mathrm{Mat}(n \times n ; \mathcal{A})$ is a quantum matrix in $\mathrm{Mat}_q(n \times n)$ iff the following ...
7
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0
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Are there attempts to numerically finding algebraic structures over finite-dimensional vector spaces?
By "algebraic structure" I mean a finite set of linear operators between tensor products of copies of one (or more) finite-dimensional (complex or real) vector spaces, fulfilling a set of ...
2
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2
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477
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Comultiplication of elements of partition of unity
Let $F(G)$ be the algebra of functions on a finite quantum group $G$ (so that $F(G)$ is a finite dimensional $\mathrm{C}^*$-Hopf algebra).
Suppose that $\{p_i:i=0,\dots,d-1\}\subset F(G)$ is a ...
8
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1
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393
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Image of Comultiplication on Finite Quantum Groups/Hopf Algebras
Let $A=:F(G)$ be the algebra of functions on a finite quantum groups aka a finite dimensional C*-Hopf Algebra.
Suppose that $F(G)$ is neither commutative nor cocommutative.
In their 1966 paper Kac and ...
1
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1
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168
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Coinvariant Subalgebras of Hopf Comodules and Quotients
For $H$ a Hopf algebra, let $V$ be a right $H$-comodule with coaction $\Delta_R$. Moreover, let $W$ be a subspace of $V$ such that $\Delta_R(W) \subseteq W \otimes H$, and note that this implies that $...