Tagged Questions

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An $SU(3)$ isomorph in Clifford $G(5,0)$?

I am a computer scientist using the geometric (Clifford) algebras $G(n,0)$ over $\mathbb{Z}_3 = \{0,1,-1\}$ to describe distributed computations. My question concerns $G(5,0)$ with generators ...
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$f:C\longrightarrow D$ coalgebra homomorphism $\Rightarrow$ $f^*:D^*\longrightarrow C^*$ algebra homomorphism

I'm trying to prove the next problem using only arrows (avoiding Sweedler's notation): If $f:C\longrightarrow D$ is a coalgebra homomorphism, then $f^*:D^*\longrightarrow C^*$ is an algebra ...
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Fusion rules and comultiplication for a Kac algebra

Let $\mathbb{A}$ be a Kac algebra (i.e. a Hopf C*-algebra) of finite dimension, and $\mathbb{A}^{*}$ its dual : Is there a formula revealing the fusion rules for the irreducible ...
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$C(G) \otimes C(G) \simeq C(G \times G)$

Let be $G$ a compact group and $C(G)$ the vector space of continue complex functions defined over $G$, $C(G):=\{f:G \to \mathbb{C}\}$, where $f$ is a continue function. How can I prove that  C(G) ...
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elementary but confounding question about integer matrices (related to hecke operators)

Let $\Gamma(N)$ denote the kernel of the reduction map $\text{SL}_2(\mathbb{Z})\rightarrow\text{SL}_2(\mathbb{Z}/N\mathbb{Z})$ Let $p$ be a prime that is $1$ mod $N$, and let $M$ be the set of ...
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What is the antipode in a Combinatorial Hopf Algebra (or graded bialgebra)?

In several papers I've seen on Combinatorial Hopf Algebras, the algebra and coalgebra structures are described, but no antipode is defined. CHAs generally have a natural grading, and are of finite ...
200 views

A simple Hopf algebra problems

I have a little question when I read an article. Someone can give me any clue? Let $\mathrm{H}$ be a Hopf algebra and $\mathrm{B}$ be a braided bialgebra in Left-left-Yetter-Drinfled-module over ...
When ever I find definition of the quantum plane it says $A_q^2 = C\langle x,y \rangle/I$, where $I = C\langle xy-qyx \rangle$. What I want to know is whether they mean the unital free algebra or just ...
Zero divisors in $SU_q(2)$
I'm looking at the quantum group $SU_q(2)$ (over ${\mathbb C}$) and can't see why it has no zero divisors. It's clear that $M_q(2)$, the quantum $2 \times 2$ matrices have no zero divisors, but I ...