dorsal/arxiv
View SchemaThe dual $(p,q)$-Alexander-Conway Hopf algebras and the associated universal ${\cal T}$-matrix
| Authors | R. Chakrabarti, R. Jagannathan |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9602020 |
| URL | https://arxiv.org/abs/q-alg/9602020 |
| DOI | 10.1007/BF02909182 |
Abstract
The dually conjugate Hopf algebras $Fun_{p,q}(R)$ and $U_{p,q}(R)$ associated with the two-parametric $(p,q)$-Alexander-Conway solution $(R)$ of the Yang-Baxter equation are studied. Using the Hopf duality construction, the full Hopf structure of the quasitriangular enveloping algebra $U_{p,q}(R)$ is extracted. The universal ${\cal T}$-matrix for $Fun_{p,q}(R)$ is derived. While expressing an arbitrary group element of the quantum group characterized by the noncommuting parameters in a representation independent way, the ${\cal T}$-matrix generalizes the familiar exponential relation between a Lie group and its Lie algebra. The universal ${\cal R}$-matrix and the FRT matrix generators, $L^{(\pm )}$, for $U_{p,q}(R)$ are derived from the ${\cal T}$-matrix.
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"abstract": "The dually conjugate Hopf algebras $Fun_{p,q}(R)$ and $U_{p,q}(R)$ associated\nwith the two-parametric $(p,q)$-Alexander-Conway solution $(R)$ of the\nYang-Baxter equation are studied. Using the Hopf duality construction, the full\nHopf structure of the quasitriangular enveloping algebra $U_{p,q}(R)$ is\nextracted. The universal ${\\cal T}$-matrix for $Fun_{p,q}(R)$ is derived. While\nexpressing an arbitrary group element of the quantum group characterized by the\nnoncommuting parameters in a representation independent way, the ${\\cal\nT}$-matrix generalizes the familiar exponential relation between a Lie group\nand its Lie algebra. The universal ${\\cal R}$-matrix and the FRT matrix\ngenerators, $L^{(\\pm )}$, for $U_{p,q}(R)$ are derived from the ${\\cal\nT}$-matrix.",
"arxiv_id": "q-alg/9602020",
"authors": [
"R. Chakrabarti",
"R. Jagannathan"
],
"categories": [
"q-alg",
"math.QA"
],
"doi": "10.1007/BF02909182",
"title": "The dual $(p,q)$-Alexander-Conway Hopf algebras and the associated universal ${\\cal T}$-matrix",
"url": "https://arxiv.org/abs/q-alg/9602020"
},
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