Title: The Derived Picard Group is a Locally Algebraic Group

Publication status: appeared in Algebras and Representation Theory 7 (2004), 53-57.

Let A be a finite dimensional algebra over an algebraically
closed field K. The derived Picard group DPic(A) is the group of
two-sided tilting complexes over A modulo isomorphism. We prove
that DPic(A) is a locally algebraic group, and its identity
component is Out^0(A). If B is a derived Morita equivalent algebra
then DPic(A) is isomorphisc to DPic(B) as locally algebraic
groups. Our results extend, and our based on, work of
Huisgen-Zimmermann and Saorin.

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(updated 25 March 2004)