2,115 research outputs found
On several varieties of cacti and their relations
Motivated by string topology and the arc operad, we introduce the notion of
quasi-operads and consider four (quasi)-operads which are different varieties
of the operad of cacti. These are cacti without local zeros (or spines) and
cacti proper as well as both varieties with fixed constant size one of the
constituting loops. Using the recognition principle of Fiedorowicz, we prove
that spineless cacti are equivalent as operads to the little discs operad. It
turns out that in terms of spineless cacti Cohen's Gerstenhaber structure and
Fiedorowicz' braided operad structure are given by the same explicit chains. We
also prove that spineless cacti and cacti are homotopy equivalent to their
normalized versions as quasi-operads by showing that both types of cacti are
semi-direct products of the quasi-operad of their normalized versions with a
re-scaling operad based on R>0. Furthermore, we introduce the notion of
bi-crossed products of quasi-operads and show that the cacti proper are a
bi-crossed product of the operad of cacti without spines and the operad based
on the monoid given by the circle group S^1. We also prove that this particular
bi-crossed operad product is homotopy equivalent to the semi-direct product of
the spineless cacti with the group S^1. This implies that cacti are equivalent
to the framed little discs operad. These results lead to new CW models for the
little discs and the framed little discs operad.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-13.abs.htm
Twisting algebras using non-commutative torsors
Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can
be used to twist comodule algebras. After surveying and extending the
literature on the subject, we prove a theorem that affords a presentation by
generators and relations for the algebras obtained by such twisting. We give a
number of examples, including new constructions of the quantum affine spaces
and the quantum tori.Comment: 27 pages. Masuoka is a new coauthor. Introduction was revised.
Sections 1 and 2 were thoroughly restructured. The presentation theorem in
Section 3 is now put in a more general framework and has a more general
formulation. Section 4 was shortened. All examples (quantum affine spaces and
tori, twisting of SL(2), twisting of the enveloping algebra of sl(2)) are
left unchange
Graded q-pseudo-differential Operators and Supersymmetric Algebras
We give a supersymmetric generalization of the sine algebra and the quantum
algebra . Making use of the -pseudo-differential operators
graded with a fermionic algebra, we obtain a supersymmetric extension of sine
algebra. With this scheme we also get a quantum superalgebra .Comment: 10 pages, Late
Cleft Extensions and Quotients of Twisted Quantum Doubles
Given a pair of finite groups and a normalized 3-cocycle of
, where acts on as automorphisms, we consider quasi-Hopf algebras
defined as a cleft extension where denotes
some suitable cohomological data. When is a
quotient of by a central subgroup acting trivially on , we give
necessary and sufficient conditions for the existence of a surjection of
quasi-Hopf algebras and cleft extensions of the type . Our
construction is particularly natural when acts on by conjugation, and
is a twisted quantum double . In
this case, we give necessary and sufficient conditions that
Rep() is a modular
tensor category.Comment: LaTex; 14 page
Some open questions on anti-de Sitter geometry
We present a list of open questions on various aspects of AdS geometry, that
is, the geometry of Lorentz spaces of constant curvature -1. When possible we
point out relations with homogeneous spaces and discrete subgroups of Lie
groups, to Teichm\"uller theory, as well as analogs in hyperbolic geometry.Comment: Not a research article in the usual sense but rather a list of open
questions. 19 page
Summer Field Day Scheduled for ISU Northern Iowa Research Farm
Crop management, nitrogen management, and crops grown for an energy source will be highlighted topics of the summer field day at the Iowa State University Northern Research and Demonstration Farm. The field day will take place June 25, at the farmâs northern location at 310 S. Main St., Kanawha, immediately south of town on county road R-35
Ambiskew Hopf algebras
Necessary and sufficient conditions are obtained for an ambiskew
polynomial algebra A over a Hopf k-algebra R to possess the structure of a
Hopf algebra extending that of R, in which the added variables X+ and X-
are skew primitive. The coradical filtration is calculated, many examples are
described, and properties determined
String-inspired Gauss-Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy
We consider scalar-Gauss-Bonnet and modified Gauss-Bonnet gravities and
reconstruct these theories from the universe expansion history. In particular,
we are able to construct versions of those theories (with and without ordinary
matter), in which the matter dominated era makes a transition to the cosmic
acceleration epoch. It is remarkable that, in several of the cases under
consideration, matter dominance and the deceleration-acceleration transition
occur in the presence of matter only. The late-time acceleration epoch is
described asymptotically by de Sitter space but may also correspond to an exact
CDM cosmology, having in both cases an effective equation of state
parameter close to -1. The one-loop effective action of modified
Gauss-Bonnet gravity on the de Sitter background is evaluated and it is used to
derive stability criteria for the ensuing de Sitter universe.Comment: LaTeX20 pages, 4 figures, version to apear in PR
Cotensor Coalgebras in Monoidal Categories
We introduce the concept of cotensor coalgebra for a given bicomodule over a
coalgebra in an abelian monoidal category. Under some further conditions we
show that such a cotensor coalgebra exists and satisfies a meaningful universal
property. We prove that this coalgebra is formally smooth whenever the comodule
is relative injective and the coalgebra itself is formally smooth
Braidings of Tensor Spaces
Let be a braided vector space, that is, a vector space together with a
solution of the Yang--Baxter equation.
Denote . We associate to a solution
of the Yang--Baxter equation on
the tensor space . The correspondence is functorial with respect to .Comment: 10 pages, no figure
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