E-Book Overview
Threading Homology through Algebra takes homological themes (Koszul complexes and their variations, resolutions in general) and shows how these affect the perception of certain problems in selected parts of algebra, as well as their success in solving a number of them. The text deals with regular local rings, depth-sensitive complexes, finite free resolutions, letter-place algebra, Schur and Weyl modules, Weyl-Schur complexes and determinantal ideals. Aimed at graduates and academics in mathematics, the book provides an overview of the developments that have taken place in these areas as well as an insight into some of the open problems which exist.
E-Book Content
OX FO R D M AT H E M AT I C A L M O N O G R A P H S Series Editors J. M. BALL W. T. GOWERS N. J. HITCHIN L. NIRENBERG R. PENROSE A. WILES OX FO R D M AT H E M AT I C A L M O N O G R A P H S Hirschfeld: Finite projective spaces of three dimensions Edmunds and Evans: Spectral theory and differential operators Pressley and Segal: Loop groups, paperback Evens: Cohomology of groups Hoffman and Humphreys: Projective representations of the symmetric groups: Q-Functions and Shifted Tableaux Amberg, Franciosi, and Giovanni: Products of groups Gurtin: Thermomechanics of evolving phase boundaries in the plane Faraut and Koranyi: Analysis on symmetric cones Shawyer and Watson: Borel’s methods of summability Lancaster and Rodman: Algebraic Riccati equations Th´ evenaz: G-algebras and modular representation theory Baues: Homotopy type and homology D’Eath: Black holes: gravitational interactions Lowen: Approach spaces: the missing link in the topology–uniformity–metric triad Cong: Topological dynamics of random dynamical systems Donaldson and Kronheimer: The geometry of four-manifolds, paperback Woodhouse: Geometric quantization, second edition, paperback Hirschfeld: Projective geometries over finite fiel