The 2-group of symmetries of a split chain complex

Details The 2-group of symmetries of a split chain complex The 2-group of symmetries of a split chain complex

2010-12-09

arxiv.org/abs/1012.1964v1

Mathematics

K-Theory and Homology

23 p

Scientific paper

We explicitly compute the 2-group of self-equivalences and (homotopy classes of) chain homotopies between them for any {\it split} chain complex $A_{\bullet}$ in an arbitrary $\kb$-linear abelian category ($\kb$ any commutative ring with unit). In particular, it is shown that it is a {\it split} 2-group whose equivalence class depends only on the homology of $A_{\bullet}$, and that it is equivalent to the trivial 2-group when $A_\bullet$ is a split exact sequence. This provides a description of the {\it general linear 2-group} of a Baez and Crans 2-vector space over an arbitrary field $\mathbb{F}$ and of its generalization to chain complexes of vector spaces of arbitrary length.

Affiliated with

Also associated with

No associations

Rating

The 2-group of symmetries of a split chain complex does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The 2-group of symmetries of a split chain complex, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The 2-group of symmetries of a split chain complex will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-76855