Locally semisimple coverings

Small Semisimple Subalgebras of Semisimple Lie Algebras

The goal of Section 2 is to provide a proof of Theorem 2.0.1. Section 3 introduces the necessary facts about Lie algebras and representation theory, with the goal being the proof of Proposition 3.5.7 (ultimately as an application of Theorem 2.0.1), and Proposition 3.3.1. In Section 4 we prove the main theorem, using Propositions 3.3.1 and 3.5.7. In Section 5, we apply the theorem to the special...

Locally semisimple and maximal subalgebras of the finitary Lie algebras gl ( ∞ ) , sl ( ∞ ) , so ( ∞ ) , and sp ( ∞ )

We describe all locally semisimple subalgebras and all maximal subalgebras of the finitary Lie algebras gl(∞), sl(∞), so(∞), and sp(∞). For simple finite–dimensional Lie algebras these classes of subalgebras have been described in the classical works of A. Malcev and E. Dynkin.

Fractional Coverings, Greedy Coverings, and Rectifier Networks

A rectifier network is a directed acyclic graph with distinguished sources and sinks; it is said to compute a Boolean matrix M that has a 1 in the entry (i, j) iff there is a path from the jth source to the ith sink. The smallest number of edges in a rectifier network that computes M is a classic complexity measure on matrices, which has been studied for more than half a century. We explore two...

Semisimple Holonomic

Maschke functors, semisimple . . . Applications

Maschke functors, semisimple functors and separable functors of the second kind. Abstract We introduce separable functors of the second kind (or H-separable functors) and H-Maschke functors. H-separable functors are generalizations of separable functors. Various necessary and sufficient conditions for a functor to be H-separable or H-Maschke, in terms of generalized (co)Casimir elements (integr...