The derived Picard group is a locally algebraic group Academic Article uri icon

abstract

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

publication date

  • March 1, 2004