Lie subalgebras of Differential Operators in one Variable

Autor:	Martin, Francisco J. Plaza, Prieto, Carlos Tejero
Rok vydání:	2019
Předmět:	Mathematics - Representation Theory Mathematical Physics Nonlinear Sciences - Exactly Solvable and Integrable Systems 17B68 (Primary) 81R10 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Let $\operatorname{Witt}$ be the Lie algebra generated by the set $\{L_i\,\vert\, i \in {\mathbb Z}\}$ and $\operatorname{Vir}$ its universal central extension. Let $\operatorname{Diff}(V)$ be the Lie algebra of differential operators on $V=\mathbb{C}[[z]]$, $\mathbb{C}((z))$ or $V=\mathbb{C}(z)$. We explicitly describe all Lie algebra homomorphisms from $\mathfrak{sl}(2)$, $\operatorname{Witt}$ and $\operatorname{Vir}$ to $\operatorname{Diff}(V)$ such that $L_0$ acts on $V$ as a first order differential operator. Comment: To appear in the Mediterranean Journal of Mathematics, Vol. 16 (2019), issue no. 6
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1905.00463 Zobrazit plný text záznamu View this record from Arxiv