Computational methods for representations of groups and algebras. Proceedings of the Euroconference in Essen, Germany, April 1--5, 1997 (Q1296344)

The articles of this volume will be reviewed individually. This book presents material from three survey lectures and 14 additional invited lectures given at the Euroconference ``Computational Methods for Representations of Groups and Algebras'' held at Essen University in April 1997. The purpose of this meeting was to provide a survey of general theoretical and computational methods and recent advances in the representation theory of groups and algebras. Furthermore, new applications of the computational methods in linear algebra to the revision of the classification of finite simple sporadic groups are presented. Computational tools (including high-performance computations on supercomputers) have become increasingly important for classification problems. They are also inevitable for the construction of projective resolutions of finitely generated modules over finite-dimensional algebras and the study of group cohomology and rings of invariants. A major part of this book is devoted to a survey of algorithms for computing special examples in the study of Grothendieck groups, quadratic forms and derived categories of finite-dimensional algebras. Open questions on Lie algebras, Bruhat orders, Coxeter groups and Kazhdan-Lusztig polynomials are investigated with the aid of computer programs. The representation theory of finite groups and finite-dimensional algebras are linked by the condensation technique. The contents of this book provide an overview on the present state of the art, for graduate students and researchers in mathematics, computer science and physics. Indexed articles: \textit{Dräxler, Peter; Nörenberg, Rainer}, Classification problems in the representation theory of finite-dimensional algebras, 3-28 [Zbl 0942.16018] \textit{Green, Edward L.}, Noncommutative Gröbner bases, and projective resolutions, 29-60 [Zbl 0957.16033] \textit{Wilson, Robert A.}, Construction of finite matrix groups, 61-83 [Zbl 0939.20011] \textit{Barot, M.; de la Peña, J. A.}, Derived tubularity: a computational approach., 87-106 [Zbl 1058.16504] \textit{Carlson, Jon F.}, Problems in the calculation of group cohomology, 107-120 [Zbl 0948.20028] \textit{Cohen, Arjeh M.; de Man, Ronald}, On a tensor category for the exceptional Lie groups, 121-137 [Zbl 0941.22012] \textit{Cojocaru, Svetlana; Podoplelov, Alexander; Ufnarovski, Victor}, Non-commutative Gröbner bases and Anick's resolution, 139-159 [Zbl 0951.16020] \textit{Cooperman, G. D.; Lempken, W.; Michler, G. O.; Weller, M.}, A new existence proof of Janko's simple group \(J_4\), 161-175 [Zbl 0949.20011] \textit{Decker, Wolfram; de Jong, Theo; Greuel, Gert-Martin; Pfister, Gerhard}, The normalization: A new algorithm, implementation and comparisons, 177-185 [Zbl 0942.13010] \textit{Dowbor, Piotr; Hübner, Thomas}, A computer algebra approach to sheaves over weighted projective lines, 187-200 [Zbl 0951.16019] \textit{du Cloux, Fokko}, Some open problems in the theory of Kazhdan-Lusztig polynomials and Coxeter groups, 201-210 [Zbl 0942.20028] \textit{Fleischmann, Peter}, Relative trace ideals and Cohen-Macaulay quotients of modular invariant rings, 211-233 [Zbl 0947.13005] \textit{Gollan, Holger W.; Havas, George}, On Sims' presentation for Lyons' simple group, 235-240 [Zbl 0936.20012] \textit{Havas, George; Sims, Charles C.}, A presentation for the Lyons simple group, 241-249 [Zbl 0936.20011] \textit{von Höhne, Hans-Joachim}, Reduction of weakly definite unit forms., 251-257 [Zbl 1037.11506] \textit{Holt, Derek F.}, Decision problems in finitely presented groups, 259-265 [Zbl 0945.20019] \textit{Kemper, Gregor; Steel, Allan}, Some algorithms in invariant theory of finite groups, 267-285 [Zbl 0954.13002] \textit{Lenzing, Helmut}, Coxeter transformations associated with finite dimensional algebras, 287-308 [Zbl 0941.16007] \textit{Müller, Jürgen; Rosenboom, Jens}, Condensation of induced representations and an application: The \(2\)-modular decomposition numbers of \(Co_2\), 309-321 [Zbl 0945.20008] \textit{Ovsienko, Serge}, Bimodule and matrix problems, 323-357 [Zbl 0948.16008]