Geometry of chain complexes and outer automorphisms under derived equivalence

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dc.creatorHuisgen-Zimmermann, Birge
dc.creatorSaorin, Manuel
dc.date2000-12-15
dc.date.accessioned2026-07-07T04:39:13Z
dc.date.available2026-07-07T04:39:13Z
dc.descriptionThe two main theorems proved here are as follows: If $A$ is a finite dimensional algebra over an algebraically closed field, the identity component of the algebraic group of outer automorphisms of $A$ is invariant under derived equivalence. This invariance is obtained as a consequence of the following generalization of a result of Voigt. Namely, given an appropriate geometrization $\text{Comp}^A_{\bold d}$ of the family of finite $A$-module complexes with fixed sequence $\bold d$ of dimensions and an ``almost projective'' complex $X\in \text{Comp}^A_{\bold d}$, there exists a canonical vector space embedding $$T_{X}(\text{Comp}^A_{\bold d}) / T_{X}(G.X) \ \longrightarrow \text{Hom}_{D^b (A\text{-Mod})}(X, X[1]),$$ where $G$ is the pertinent product of general linear groups acting on $\text{Comp}^A_{\bold d}$, tangent spaces at $X$ are denoted by $T_X(-)$, and $X$ is identified with its image in the derived category $D^b (A\text{-Mod})$.
dc.description21 pages. To appear in Trans. Amer. Math. Soc
dc.identifierhttps://arxiv.org/abs/math/0012119
dc.identifierhttp://arxiv.org/abs/math/0012119
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60573
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.subject16E05, 16G10, 16P10, 18E30, 18G35
dc.titleGeometry of chain complexes and outer automorphisms under derived equivalence
dc.typetext

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