dorsal/arxiv
View SchemaOn classification of dynamical r-matrices
| Authors | Olivier Schiffmann |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9706017 |
| URL | https://arxiv.org/abs/q-alg/9706017 |
Abstract
Using recent results of P. Etingof and A. Varchenko on the Classical Dynamical Yang-Baxter equation, we reduce the classification of dynamical r-matrices r on a commutative subalgebra l of a Lie algebra g to a purely algebraic problem under some technical conditions on the symmetric part of r. Using this, we then classify all non skew-symmetric dynamical r-matrices when g is a simple Lie algebra and l a commutative subalgebra containing a regular semisimple element. This partially answers a question in [EV] q-alg/9703040 and generalizes the Belavin-Drinfeld classification of constant r-matrices. This classification is similar and in some sense simpler than the Belavin-Drinfeld classification.
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"abstract": "Using recent results of P. Etingof and A. Varchenko on the Classical\nDynamical Yang-Baxter equation, we reduce the classification of dynamical\nr-matrices r on a commutative subalgebra l of a Lie algebra g to a purely\nalgebraic problem under some technical conditions on the symmetric part of r.\nUsing this, we then classify all non skew-symmetric dynamical r-matrices when g\nis a simple Lie algebra and l a commutative subalgebra containing a regular\nsemisimple element. This partially answers a question in [EV] q-alg/9703040 and\ngeneralizes the Belavin-Drinfeld classification of constant r-matrices. This\nclassification is similar and in some sense simpler than the Belavin-Drinfeld\nclassification.",
"arxiv_id": "q-alg/9706017",
"authors": [
"Olivier Schiffmann"
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"title": "On classification of dynamical r-matrices",
"url": "https://arxiv.org/abs/q-alg/9706017"
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