dorsal/arxiv
View SchemaReflection Equation Algebra of a $(h,w)$-deformed Oscillator
| Authors | Boucif Abdesselam, Ranabir Chakrabarti |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9706032 |
| URL | https://arxiv.org/abs/q-alg/9706032 |
Abstract
We consider the reflection equation algebra for a finite dimensional R-matrix for the $(h,w)$-deformed Heisenberg algebra ${\cal U}_{h,w}(h(4))$. A representation of the reflection matrix $K$ is constructed using the matrix generators $L^{(\pm)}$ of the ${\cal U}_{h,w}(h(4))$ algebra. A series of representations of the K-matrix then may be generated by using the coproduct rules of the ${\cal U}_{h,w}(h(4))$ algebra. The complementary condition necessary for combining two distinct solutions of the reflection equation algebra yields the braiding relations between these two sets of generators. This may be thought as a generalization of Bose-Fermi statistics to braiding statistics, which them may be used to provide a new braided colagebraic structure to a Hopf algebra generated by the elements of the matrix $K$. The reflection equation algebra and the braided exchange properties are found to depend on both deformation parameters $h$ and $w$.
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"abstract": "We consider the reflection equation algebra for a finite dimensional R-matrix\nfor the $(h,w)$-deformed Heisenberg algebra ${\\cal U}_{h,w}(h(4))$. A\nrepresentation of the reflection matrix $K$ is constructed using the matrix\ngenerators $L^{(\\pm)}$ of the ${\\cal U}_{h,w}(h(4))$ algebra. A series of\nrepresentations of the K-matrix then may be generated by using the coproduct\nrules of the ${\\cal U}_{h,w}(h(4))$ algebra. The complementary condition\nnecessary for combining two distinct solutions of the reflection equation\nalgebra yields the braiding relations between these two sets of generators.\nThis may be thought as a generalization of Bose-Fermi statistics to braiding\nstatistics, which them may be used to provide a new braided colagebraic\nstructure to a Hopf algebra generated by the elements of the matrix $K$. The\nreflection equation algebra and the braided exchange properties are found to\ndepend on both deformation parameters $h$ and $w$.",
"arxiv_id": "q-alg/9706032",
"authors": [
"Boucif Abdesselam",
"Ranabir Chakrabarti"
],
"categories": [
"q-alg",
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],
"title": "Reflection Equation Algebra of a $(h,w)$-deformed Oscillator",
"url": "https://arxiv.org/abs/q-alg/9706032"
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