TITLE

The variety of chain complexes

AUTHOR(S)
Darmajid
PUB. DATE
May 2012
SOURCE
AIP Conference Proceedings;5/22/2012, Vol. 1450 Issue 1, p368
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let modΛd be a category of all d-dimensional left modules over finitely generated K-algebra Λ where K is the algebraically closed field. By the same idea identifying the points of modΛd with points in HomK(Λ, EndK(Kd)), we parameterize finite chain complexes X• with points in compΛd with fixed sequence d = (dimXn, ..., dimX0 of dimensions. In this paper we will show that compΛd is an affine variety and give a proof of the following observation in Saorin and Huisgen-Zimmermann that the natural map from compΛd to the collection of complexes X• with fixed sequences d dimensions identifies the orbits of the GLd(K)-action on compΛd with the isomorphism classes of complexes of the described format in the other.
ACCESSION #
75526988

 

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