Homological algebra and module theory constitute a vibrant area of contemporary mathematics, interweaving concepts from algebra, topology and geometry. At its core, homological algebra studies ...

Roman Bezrukavnikov, Ivan Mirković, Dmitriy Rumynin, Simon Riche, Localization of Modules for a Semisimple Lie Algebra in Prime Characteristic, Annals of Mathematics, Second Series, Vol. 167, No. 3 ...

The Virasoro vertex algebra arises as the symmetry algebra of a two-dimensional conformal field theory. The Virasoro irreducible modules are well-known, and they play a prominent role in rational ...

Let p be a prime number and let GLn be the group of all invertible matrices over the prime field Fp. It is known that every irreducible GLn- module can occur as a submodule of P, the polynomial ...

Before you start, it may be helpful to read the guides on coordinates and graphs from Module 2 (M2) and Module 3 (M3). When two lines are perpendicular, the product of their gradients is 1. Lines ...

An algebraic fraction is a fraction with algebraic terms in the numerator or the denominator or both.