30 citations · 41 across the 6 of their papers we have counts for
6 papers
A Koszul category of representations of finitary Lie algebras
Elizabeth Dan-Cohen, Ivan Penkov, Vera Serganova
We find for each simple finitary Lie algebra a category of integrable modules in which the tensor product of copies of the natural and cona…
Levi components of parabolic subalgebras of finitary Lie algebras
Elizabeth Dan-Cohen, Ivan Penkov
We characterize locally semisimple subalgebras of $\sl_\infty$, $\so_\infty$, and $\sp_\infty$ which are Levi components of parabolic subalgebras. Given , we characterize th…
Parabolic and Levi subalgebras of finitary Lie algebras
Elizabeth Dan-Cohen, Ivan Penkov
Let $\g$ be a locally reductive complex Lie algebra which admits a faithful countable-dimensional finitary representation . Such a Lie algebra is a split extension of an abelian…
Parabolic Subgroups of Real Direct Limit Groups
Elizabeth Dan-Cohen, Ivan Penkov, Joseph A. Wolf
Let be a classical real direct limit Lie group and its Lie algebra. The parabolic subalgebras of the complexification were described by the first two authors. In…
Borel subalgebras of root-reductive Lie algebras
Elizabeth Dan-Cohen
This paper generalizes the classification in a paper of Dimitrov and Penkov of Borel subalgebras of gl_infty. Root-reductive Lie algebras are direct limits of finite-dimensional re…
Cartan subalgebras of root-reductive Lie algebras
Elizabeth Dan-Cohen, Ivan Penkov, Noah Snyder
Root-reductive Lie algebras are direct limits of finite-dimensional reductive Lie algebras under injections which preserve the root spaces. It is known that a root-reductive Lie al…