Solution of a Non-domestic Tame Classification Problem from Integral Representation Theory of Finite Groups (Memoirs of the AMS) (Memoirs of the American Mathematical Society) - Softcover

Dieterich, Ernst

Softcover

ISBN 10: 0821825216 ISBN 13: 9780821825211

Publisher: American Mathematical Society, 1992

Synopsis

Suppose R is a complete discrete valuation ring with exponential valuation v, G is a finite p-group. The representation type (finite, tame, or wild) of the group ring Λ = RG had been determined in all cases but one; the case in which G = C3 and v(3)=4. The present book closes this gap.

The author presents an explicit classification of all indecomposable lattices, as well as a description of the Auslander-Reiten quiver of Λ, demonstrating that this is the only integral group ring whose representation type is non-domestic tame of finite growth. This book acquaints readers with various (by now classical) tame module categories, with techniques of matrix reduction, and with the interaction of basefree (category-theoretic) and base-dependent (matrix-theoretic) viewpoints
and their respective relations to the combinatorial intuition provided by Auslander-Reiten quivers.

Edition details

• Publisher: American Mathematical Society
• Publication date: 1992
• Language: English
• ISBN 10: 0821825216
• ISBN 13: 9780821825211
• Binding: Paperback
• Number of pages: 140