## Algebras and Modules OneThis volume contains recent results on geometric aspects of representations of algebras, a thorough treatment of the theory of quasitilted algebras, new developments on infinite dimensional representations of finite dimensional algebras, a bridge between representation of algebraic groups and representation theory of finite dimensional algebras, and recent discoveries on modular representation theory. In addition, the volume contains two papers devoted to some of Maurice Auslander's many contributions both in the representation theory of finite dimensional algebras and in commutative ring theory.The invited contributions to this volume are based on lectures given by leading researchers in the field at the Workshop on Representations of Algebras and Related Topics, Trondheim, Norway. It features: a unique collection of survey papers containing old and new developments in the representation theory of finite dimensional algebras and related topics; an outstanding source for examples of different techniques developed in recent years in this area of research; papers presented with emphasis on clarity and readability; and a general background in noncommutative algebra including rings, modules and homological algebra is required. Given that, parts of this volume would be suitable as a textbook for an advanced graduate course in algebra. |

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### Contents

Some geometric aspects of representation theory | 1 |

in the representation theory of finitedimensional algebras | 29 |

Quasitilted Algebras | 55 |

Auslanders work on artin algebras | 83 |

SOME FINITE DIMENSIONAL ALGEBRAS ARISING IN GROUP THEORY | 107 |

Some Recent Advances in Modular Representation Theory | 157 |

Auslanders work on CohenMacaulay modules and recent development | 179 |

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### Common terms and phrases

A G A A-mod A-module abelian category algebraic group algebraically compact modules artin algebras assume Auslander Auslander-Reiten quiver block algebras coherent functors components corresponding defined definition degenerations denote Department of Mathematics derived categories derived equivalent dimension dimensional modules direct sum direct summand endofinite endomorphism algebra exact sequence example exists filtration finite dimensional algebra finite group finite-dimensional modules full subcategory functor F geometric quotient hence hereditary abelian category Hom(X homomorphism idempotent indecomposable modules infinite injective irreducible isomorphism classes Kazhdan-Lusztig Krull dimension lemma Let H matrix morphism non-zero open subset orbit polynomial poset preprojective principal blocks projective modules proof quasi-hereditary algebras quasi-simple quasitilted algebra Reiten representation theory representation-finite resp result ring satisfying simple modules split sequences split torsion pair stable equivalence stable module category stratification subfunctor subgroup submodule surjective theorem tilted algebras tilting complex tilting module tilting object triangulated categories vector