34 research outputs found
An explicit description of the simplicial group
We give a new explicit construction for the simplicial group . We
explain the topological interpretation and discuss some possible applications.Comment: 8 page
Secondary Cohomology and k-invariants
For a triple (where is a group, is a -module and
is a 3-cocycle) and a -module we introduce a new
cohomology theory which we call the secondary cohomology.
We give a construction that associates to a pointed topological space
an invariant . This
construction can be seen a "3-type" generalization of the classical
-invariant.Comment: 8 page
Symmetric cohomology of groups in low dimension
We give an explicit characterization for group extensions that correspond to
elements of the symmetric cohomology . We also give conditions for
the map to be injective
From 3-algebras to -Groups
We introduce -groups and show how they fit in the context of lattice
field theory. To a manifold we associate a -group . We
define the symmetric cohomology of a group with coefficients in
a -module . The -group is determined by the action of
on and an element of .Comment: 18 page
Operations on the Secondary Hochschild Cohomology
We show that the secondary Hochschild cohomology associated to a triple
has several of the properties of the usual Hochschild
cohomology. Among others, we prove the existence of the cup and Lie products,
discuss the connection with extensions of -algebras, and give a Hodge type
decomposition of the secondary Hochschild cohomology
-Algebra Structure on the Higher Order Hochschild Cohomology
We present a deformation theory associated to the higher Hochschild
cohomology . We also study a -algebra structure associated
to this deformation theory
Generalized (anti) Yetter-Drinfeld modules as components of a braided T-category
If H is a Hopf algebra with bijective antipode and \alpha, \beta \in
Aut_{Hopf}(H), we introduce a category_H{\cal YD}^H(\alpha, \beta),
generalizing both Yetter-Drinfeld and anti-Yetter-Drinfeld modules. We
construct a braided T-category {\cal YD}(H) having all these categories as
components, which if H is finite dimensional coincides with the representations
of a certain quasitriangular T-coalgebra DT(H) that we construct. We also prove
that if (\alpha, \beta) admits a so-called pair in involution, then_H{\cal
YD}^H(\alpha, \beta) is isomorphic to the category of usual Yetter-Drinfeld
modules_H{\cal YD}^H.Comment: 12 pages, Latex, no figure
Hom-Tensor Categories and the Hom-Yang-Baxter Equation
We introduce a new type of categorical object called a \emph{hom-tensor
category} and show that it provides the appropriate setting for modules over an
arbitrary hom-bialgebra. Next we introduce the notion of \emph{hom-braided
category} and show that this is the right setting for modules over
quasitriangular hom-bialgebras. We also show how the hom-Yang-Baxter equation
fits into this framework and how the category of Yetter-Drinfeld modules over a
hom-bialgebra with bijective structure map can be organized as a hom-braided
category. Finally we prove that, under certain conditions, one can obtain a
tensor category (respectively a braided tensor category) from a hom-tensor
category (respectively a hom-braided category).Comment: 36 pages, many diagram
Bar Simplicial Modules and Secondary Cyclic (Co)homology
In this paper we study the simplicial structure of the complex
, associated to the secondary Hochschild
cohomology. The main ingredient is the simplicial object
, which plays a role equivalent to that of the
bar resolution associated to an algebra. We also introduce the secondary cyclic
(co)homology and establish some of its properties (Theorems 3.9 and 4.11).Comment: 17 page
The Exterior Graded Swiss-Cheese Operad (with an appendix by Ana Lorena Gherman and Mihai D. Staic)
In this paper we present a construction which is a generalization of the
exterior algebra of a vector space . We show how this fits in the language
of operads, discuss some properties, and give explicit computations for the
case .Comment: 12 page