4,673 research outputs found
Hochschild cohomology via incidence algebras
Given an algebra A we associate an incidence algebra A(\Sigma) and compare
their Hochschild cohomology groups.Comment: 16 pages, Section 3.2 deleted, Section 4 adde
Cartan-Leray spectral sequence for Galois coverings of linear categories
We provide a Cartan-Leray type spectral sequence for the Hochschild-Mitchell
(co)homology of a Galois covering of linear categories. We infer results
relating the Galois group and Hochschild cohomology in degree one
Cohomology of the Grothendieck construction
We consider cohomology of small categories with coefficients in a natural
system in the sense of Baues and Wirsching. For any funtor L: K -> CAT, we
construct a spectral sequence abutting to the cohomology of the Grothendieck
construction of L in terms of the cohomology of K and of L(k), for k an object
in K.Comment: 13 page
On the first Hochschild cohomology group of a cluster-tilted algebra
Given a cluster-tilted algebra B, we study its first Hochschild cohomology
group HH^1(B) with coefficients in the B-B-bimodule B. If C is a tilted algebra
such that B is the relation extension of C, then we show that if C is
constrained, or else if B is tame, then HH^1(B) is isomorphic, as a k-vector
space, to the direct sum of HH^1(C) with k^{n\_{B,C}}, where n\_{B,C} is an
invariant linking the bound quivers of B and C. In the representation-finite
case, HH^1(B) can be read off simply by looking at the quiver of B.Comment: 30 page
On universal gradings, versal gradings and Schurian generated categories
Categories over a field can be graded by different groups in a connected
way; we consider morphisms between these gradings in order to define the
fundamental grading group. We prove that this group is isomorphic to the
fundamental group \`a la Grothendieck as considered in previous papers. In case
the -category is Schurian generated we prove that a universal grading
exists. Examples of non Schurian generated categories with universal grading,
versal grading or none of them are considered.Comment: Final version to appear in the Journal of Noncommutative Geometry, 21
page
Fundamental group of Schurian categories and the Hurewicz isomorphism
Let k be a field. We attach a CW-complex to any Schurian k-category and we
prove that the fundamental group of this CW-complex is isomorphic to the
intrinsic fundamental group of the k-category. This extends previous results by
J.C. Bustamante. We also prove that the Hurewicz morphism from the vector space
of abelian characters of the fundamental group to the first Hochschild-Mitchell
cohomology vector space of the category is an isomorphism.Comment: Final version to appear in Documenta Mathematica, 14 page
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