dorsal/arxiv
View SchemaClassification of Bicovariant Differential Calculi on the Quantum Groups $SL_q(n+1)$ and $Sp_q(2n)$
| Authors | I. Heckenberger, K. Schmuedgen |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9707032 |
| URL | https://arxiv.org/abs/q-alg/9707032 |
Abstract
For transcendental values of $q$ all bicovariant first order differential calculi on the coordinate Hopf algebras of the quantum groups $SL_q(n+1)$ and $Sp_q(2n)$ are classified. It is shown that the irreducible bicovariant first order calculi are determined by an irreducible corepresentation of the quantum group and a complex number $\zeta$ such that $\zeta^{n+1}=1$ for $SL_q(n+1)$ and $\zeta^2=1$ for $Sp_q(2n)$. Any bicovariant calculus is inner and its quantum Lie algebra is generated by a central element. The main technical ingredient is a result of the Hopf algebra $R(G_q)^0$ for arbitrary simple Lie algebras.
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"abstract": "For transcendental values of $q$ all bicovariant first order differential\ncalculi on the coordinate Hopf algebras of the quantum groups $SL_q(n+1)$ and\n$Sp_q(2n)$ are classified. It is shown that the irreducible bicovariant first\norder calculi are determined by an irreducible corepresentation of the quantum\ngroup and a complex number $\\zeta$ such that $\\zeta^{n+1}=1$ for $SL_q(n+1)$\nand $\\zeta^2=1$ for $Sp_q(2n)$. Any bicovariant calculus is inner and its\nquantum Lie algebra is generated by a central element. The main technical\ningredient is a result of the Hopf algebra $R(G_q)^0$ for arbitrary simple Lie\nalgebras.",
"arxiv_id": "q-alg/9707032",
"authors": [
"I. Heckenberger",
"K. Schmuedgen"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Classification of Bicovariant Differential Calculi on the Quantum Groups $SL_q(n+1)$ and $Sp_q(2n)$",
"url": "https://arxiv.org/abs/q-alg/9707032"
},
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