Date:	Thu, April 6, 2017
Time:	11:30
Place:	Seminar Room (120), Research I

Abstract: A root-reductive Lie algebra \(\mathfrak{g}\) is an inductive limit of finite-dimensional reductive Lie algebras \(\lim\limits_{\longrightarrow}\,\mathfrak{g}_n\) satisfying the property that each embedding \(\mathfrak{g}_n\hookrightarrow\mathfrak{g}_{n+1}\) is a root inclusion. Examples of root-reductive Lie algebras include the simple finitary Lie algebras \(\mathfrak{sl}_\infty(\mathbb{C})\), \(\mathfrak{so}_\infty(\mathbb{C})\), and \(\mathfrak{sp}_\infty(\mathbb{C})\), as well as the Lie algebra \(\mathfrak{gl}_\infty(\mathbb{C})\). In this talk, we shall discuss the properties of toral subalgebras, Cartan subalgebras, and Borel subalgebras of a root-reductive Lie algebra. The talk is based on two papers: [Dan-Cohen, Penkov, and Snyder] and [Dan-Cohen].