Skip to main content

All Questions

Filter by
Sorted by
Tagged with
1 vote
0 answers
122 views

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 ...
Joe's user avatar
  • 545
7 votes
0 answers
116 views

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 ...
Andi Bauer's user avatar
  • 3,001
2 votes
2 answers
477 views

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 ...
JP McCarthy's user avatar
  • 1,027
8 votes
1 answer
393 views

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 ...
JP McCarthy's user avatar
  • 1,027
1 vote
1 answer
168 views

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 $...
Ago Szekeres's user avatar