Universität zu Köln

Burban, Igor and Henrich, Thilo (2015). Vector bundles on plane cubic curves and the classical Yang-Baxter equation. J. Eur. Math. Soc., 17 (3). S. 591 - 645. ZURICH: EUROPEAN MATHEMATICAL SOC. ISSN 1435-9855

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Abstract

In this article, we develop a geometric method to construct solutions of the classical Yang-Baxter equation, attaching a family of classical r-matrices to the Weierstrass family of plane cubic curves and a pair of coprime positive integers. It turns out that all elliptic r-matrices arise in this way from smooth cubic curves. For the cuspidal cubic curve, we prove that the solutions obtained are rational and compute them explicitly. We also describe them in terms of Stolin's classification and prove that they are degenerations of the corresponding elliptic solutions.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Burban, Igor UNSPECIFIED UNSPECIFIED UNSPECIFIED Henrich, Thilo UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-416817
DOI:	10.4171/JEMS/512
Journal or Publication Title:	J. Eur. Math. Soc.
Volume:	17
Number:	3
Page Range:	S. 591 - 645
Date:	2015
Publisher:	EUROPEAN MATHEMATICAL SOC
Place of Publication:	ZURICH
ISSN:	1435-9855
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language RATIONAL SOLUTIONS; PROJECTIVE CURVES Multiple languages Mathematics, Applied; Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/41681