Bol three-webs with covariant constant curvature tensor

A. M. Shelekhov ; E. A. Onoprienko

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2016), pp. 82-92.

Résumé

We find complete system of tensor relations characterizing the class of multidimensional middle Bol three-webs with covariant constant curvature tensor and ascertain the algebraic sense of these relations. We prove the existence of such webs and lay the foundation of their classification in terms of torsion tensor rank. We show that $6$-dimensional non-group webs of such type are the known flexible webs $E_1$ and $E_2$.

Détail

Keywords: three-web, middle Bol three-web, flexible three-web, $W$-algebra, Chern connection of a three-web, commutator, holonomy algebra.
Mots-clés : associator

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