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 chain ...

Annals of Mathematics, Second Series, Vol. 167, No. 3 (May, 2008), pp. 945-991 (47 pages) We show that, on the level of derived categories, representations of the Lie algebra of a semisimple algebraic ...

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 A ...

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 ...

The same method is used for adding / subtracting both numerical fractions and algebraic fractions. Find a common denominator Write each fraction as an equivalent fraction with the common denominator ...