WoG 2024 Talk 3.6: Nishant Rathee - Rota–Baxter operators and skew brace structures over Heisenbe…

Speaker: Nishant Rathee
Institution: IISER Mohali

Title: Rota–Baxter operators and skew brace structures over Heisenberg Group
Abstract: In this talk, we will discuss the relationship between skew left braces and Rota–Baxter operators. Skew left braces are well-known for inducing non-degenerate solutions to the Yang-Baxter equation. As an application, we classify certain skew left brace structures over the three-dimensional Heisenberg Lie group. This classification involves first identifying all Rota–Baxter operators of weight 1 on the Heisenberg Lie algebra by solving the defining equations. We then transfer these operators to the Heisenberg Lie group, utilizing the fact that the exponential map from the Heisenberg Lie algebra to the Heisenberg group is bijective.

Видео WoG 2024 Talk 3.6: Nishant Rathee - Rota–Baxter operators and skew brace structures over Heisenbe… канала World of GroupCraft