Theory of Finite Pseudoalgebras

Conformal algebras, recently introduced by Kac, encode an axiomatic description of the singular part of the operator product expansion in conformal field theory. The objective of this paper is to develop the theory of ``multi-dimensional'' analogues of conformal algebras. They are defined as Lie algebras in a certain ``pseudotensor'' category instead of the category of vector spaces. A pseudotensor category (as introduced by Lambek, and by Beilinson and Drinfeld) is a category equipped with ``polylinear maps'' and a way to compose them. This allows for the definition of Lie algebras, representations, cohomology, etc. An instance of such a category can be constructed starting from any cocommutative (or more generally, quasitriangular) Hopf algebra $H$. The Lie algebras in this category are called Lie $H$-pseudoalgebras. The main result of this paper is the classification of all simple and all semisimple Lie $H$-pseudoalgebras which are finitely generated as $H$-modules. We also start developing the representation theory of Lie pseudoalgebras; in particular, we prove analogues of the Lie, Engel, and Cartan-Jacobson Theorems. We show that the cohomology theory of Lie pseudoalgebras describes extensions and deformations and is closely related to Gelfand-Fuchs cohomology. Lie pseudoalgebras are closely related to solutions of the classical Yang-Baxter equation, to differential Lie algebras (introduced by Ritt), and to Hamiltonian formalism in the theory of nonlinear evolution equations. As an application of our results, we derive a classification of simple and semisimple linear Poisson brackets in any finite number of indeterminates.Comment: 102 pages, 7 figures, AMS late

Who Lives, Who Dies, Who Tells Your Story? A Marxist Analysis of Hamilton and its Relationship to the Broadway Economic System

Lin-Manuel Miranda’s mega-hit Hamilton: An American Musical has been both a critical and academic darling since its premiere in 2015. A historical retelling of America’s inception through the eyes of an oft-ignored founding father, the musical weaves together a diverse cast and hip-hop musical stylings in order to tell the story of “America then, as told by America now.” While many critics and scholars alike have praised the musical for putting an exciting and accessible twist to American history, others have argued that the musical is not nearly as “revolutionary” as it claims to be. This essay is designed to provide a critical analysis of Hamilton against the backdrop of existing scholarship on the musical. Specifically, examines Hamilton through the lens of Marxist literary critique in order to answer the question: who does Hamilton really represent, and how does this reflect the economic culture of Broadway

Who Lives, Who Dies, Who Tells Your Story? A Marxist Analysis of Hamilton and its Relationship to the Broadway Economic System

Lin-Manuel Miranda’s mega-hit Hamilton: An American Musical has been both a critical and academic darling since its premiere in 2015. A historical retelling of America’s inception through the eyes of an oft-ignored founding father, the musical weaves together a diverse cast and hip-hop musical stylings in order to tell the story of “America then, as told by America now.” While many critics and scholars alike have praised the musical for putting an exciting and accessible twist to American history, others have argued that the musical is not nearly as “revolutionary” as it claims to be. This essay is designed to provide a critical analysis of Hamilton against the backdrop of existing scholarship on the musical. Specifically, examines Hamilton through the lens of Marxist literary critique in order to answer the question: who does Hamilton really represent, and how does this reflect the economic culture of Broadway