dorsal/arxiv
View SchemaSome Remarks on Producing Hopf Algebras
| Authors | A. A. Vladimirov |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9507012 |
| URL | https://arxiv.org/abs/q-alg/9507012 |
| DOI | 10.1007/BF01688822 |
Abstract
We report some observations concerning two well-known approaches to construction of quantum groups. Thus, starting from a bialgebra of inhomogeneous type and imposing quadratic, cubic or quartic commutation relations on a subset of its generators we come, in each case, to a q-deformed universal enveloping algebra of a certain simple Lie algebra. An interesting correlation between the order of initial commutation relations and the Cartan matrix of the resulting algebra is observed. Another example demonstrates that the bialgebra structure of sl_q(2) can be completely determined by requiring the q-oscillator algebra to be its covariant comodule, in analogy with Manin's approach to define SL_q(2) as a symmetry algebra of the bosonic and fermionic quantum planes.
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"abstract": "We report some observations concerning two well-known approaches to\nconstruction of quantum groups. Thus, starting from a bialgebra of\ninhomogeneous type and imposing quadratic, cubic or quartic commutation\nrelations on a subset of its generators we come, in each case, to a q-deformed\nuniversal enveloping algebra of a certain simple Lie algebra. An interesting\ncorrelation between the order of initial commutation relations and the Cartan\nmatrix of the resulting algebra is observed. Another example demonstrates that\nthe bialgebra structure of sl_q(2) can be completely determined by requiring\nthe q-oscillator algebra to be its covariant comodule, in analogy with Manin\u0027s\napproach to define SL_q(2) as a symmetry algebra of the bosonic and fermionic\nquantum planes.",
"arxiv_id": "q-alg/9507012",
"authors": [
"A. A. Vladimirov"
],
"categories": [
"q-alg",
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"doi": "10.1007/BF01688822",
"title": "Some Remarks on Producing Hopf Algebras",
"url": "https://arxiv.org/abs/q-alg/9507012"
},
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