Generating functions for the coefficients of the Cremmer-Gervais R-matrices

Authors
Hodges, TJ
Citation
Tj. Hodges, Generating functions for the coefficients of the Cremmer-Gervais R-matrices, J PURE APPL, 157(1), 2001, pp. 69-79
Citations number
12
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF PURE AND APPLIED ALGEBRA
ISSN journal
00224049 → ACNP
Volume
157
Issue
1
Year of publication
2001
Pages
69 - 79
Database
ISI
SICI code
0022-4049(20010308)157:1<69:GFFTCO>2.0.ZU;2-9
Abstract
The coefficients of certain operators on V x V can be constructed using gen erating functions. Necessary and sufficient conditions are given for some s uch operators to satisfy the Yang-Baxter equation. As a corollary we obtain a simple, direct proof that the Cremmer-Gervais R-matrices satisfy the Yan g-Baxter equation. This approach also clarifies Cremmer and Gervais's origi nal proof via the dynamical Yang-Baxter equation. (C) 2001 Elsevier Science B.V. All rights reserved. MSC: Primary 81R50; secondary 17B37; 20G42; 16W3 5.