2017
DOI: 10.1088/1751-8121/aa8e35
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Simple vector bundles on a nodal Weierstrass cubic and quasi-trigonometric solutions of the classical Yang–Baxter equation

Abstract: In this paper we study the combinatorics of quasi-trigonometric solutions of the classical Yang-Baxter equation, arising from simple vector bundles on a nodal Weierstraß cubic.

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Cited by 6 publications
(11 citation statements)
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“…to the identity (15). It follows that x, a i 1 ...i n ] ∈ J for any x ∈ L, implying that J is an ideal in L. However, L does not contain any non-zero finite-dimensional ideals; see [31,Lemma 8.6].…”
Section: Basic Facts On Affine Lie Algebrasmentioning
confidence: 99%
See 2 more Smart Citations
“…to the identity (15). It follows that x, a i 1 ...i n ] ∈ J for any x ∈ L, implying that J is an ideal in L. However, L does not contain any non-zero finite-dimensional ideals; see [31,Lemma 8.6].…”
Section: Basic Facts On Affine Lie Algebrasmentioning
confidence: 99%
“…We define a nodal Weierstraß curve E via the pushout diagram (76). We recall now the description of the sheaf A given in [15,Proposition 3.3] (see also [17,Section 5.1.2]).…”
Section: Consider the Embedding Of Lie Algebras Gθmentioning
confidence: 99%
See 1 more Smart Citation
“…Distinguished quasi-trigonometric solutions of the classical Yang-Baxter equation are found in [38]. The q-deformation of maximally extended sl(2|2) is investigated by means of a contraction limit in [39].…”
Section: Quantum Groupsmentioning
confidence: 99%
“…• We answer questions one and two posed at the end of [8] concerning an explicit formula for the quasi-trigonometric solution given by a BD quadruple Q and its connection with the trigonometric solution described by the same quadruple Q (see [3]).…”
Section: Introductionmentioning
confidence: 99%