Journal of Nonlinear Mathematical Physics

Volume 21, Issue 4, October 2014, Pages 543 - 583

On deformation and classification of ∨-systems

Authors
V. Schreiber
Department of Mathematical Sciences, Loughborough University Loughborough LE11 3TU, UK, V.Schreiber@gmx.com
A.P. Veselov
Department of Mathematical Sciences, Loughborough University Loughborough LE11 3TU, UK
Moscow State University, Moscow 119899, Russia, A.P.Veselov@lboro.ac.uk
Received 6 May 2014, Accepted 31 July 2014, Available Online 6 January 2021.
DOI
https://doi.org/10.1080/14029251.2014.975528How to use a DOI?
Keywords
Root systems, ∨-systems, WDVV equation
Abstract

The ∨-systems are special finite sets of covectors which appeared in the theory of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. Several families of ∨-systems are known, but their classification is an open problem. We derive the relations describing the infinitesimal deformations of ∨-systems and use them to study the classification problem for ∨-systems in dimension three. We discuss also possible matroidal structures of ∨-systems in relation with projective geometry and give the catalogue of all known irreducible rank three ∨-systems.

Copyright
© 2014 The Author(s). Published by Taylor & Francis.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
21 - 4
Pages
543 - 583
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1080/14029251.2014.975528How to use a DOI?
Copyright
© 2014 The Author(s). Published by Taylor & Francis.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - V. Schreiber
AU  - A.P. Veselov
PY  - 2021
DA  - 2021/01
TI  - On deformation and classification of ∨-systems
JO  - Journal of Nonlinear Mathematical Physics
SP  - 543
EP  - 583
VL  - 21
IS  - 4
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2014.975528
DO  - https://doi.org/10.1080/14029251.2014.975528
ID  - Schreiber2021
ER  -