\title[Dimensions of triangulated categories]{Dimensions of triangulated categories via \\
  Koszul objects}

\thanks{Version from June 15, 2008.} 

\thanks{Bergh and Oppermann were supported by NFR Storforsk grant no. 167130, and Iyengar
  was partly supported by NSF grant, DMS 0602498. Iyengar's work was done at the
  University of Paderborn, on a visit supported by a For\-schungs\-preis awarded by the
  Humboldt-Stiftung.}

\author[Bergh]{Petter Andreas Bergh}
\address{Petter Andreas Bergh\\ Institutt for matematiske fag \\
  NTNU \\ N-7491 Trondheim \\ Norway}

\author[Iyengar]{Srikanth B. Iyengar}
\address{Srikanth B. Iyengar\\ Department of Mathematics\\
University of Nebraska\\ Lincoln NE 68588\\ U.S.A.}

\author[Krause]{\\ Henning Krause}
\address{Henning Krause\\ Institut f\"ur Mathematik\\
Universit\"at Paderborn\\ 33095 Paderborn\\ Germany.}

\author[Oppermann]{Steffen Oppermann}
\address{Steffen Oppermann\\ Institutt for matematiske fag \\
  NTNU \\ N-7491 Trondheim \\ Norway}

\subjclass[2000]{16E30, 16E40, 18E30}

\keywords{triangulated category, Koszul object, representation
dimension}

\begin{abstract}
Lower bounds for the dimension of a triangulated category are
provided.  These bounds are applied to stable derived categories of
Artin algebras and of commutative complete intersection local
rings. As a consequence, one obtains bounds for the representation
dimensions of certain Artin algebras.
\end{abstract}