Yamaguti algebras, noncrossing partitions and sl_2

Speaker: Prof. Vladimir Dotsenko，Université de Strasbourg & AMSS         

Title: Yamaguti algebras, noncrossing partitions and sl_2

Language: English

Time & Venue: 2026.09.17  15:30-17:00  南楼N202 

Abstract: Last year, A. Das introduced an algebraic structure that he called associative-Yamaguti algebras, which are supposed to serve as envelopes of the rather mysterious Lie-Yamaguti algebras, a structure arising in studying relations between the torsion and the curvature tensors of a connection in the tangent bundle of a manifold under the condition that both of these tensors are constant.

In a joint work with Chapoton, I found two rather remarkable relationships of these associative-Yamaguti algebras to completely different mathematical topics, the combinatorics of noncrossing partitions and the representation theory of the Lie algebra sl_2. In my talk, I shall explain these results. Time permitting, I shall discuss an analogue of the second result for the quantum group U_q(sl_2).