42,103 research outputs found
On Koszulity for operads of Conformal Field Theory
We study two closely related operads: the Gelfand-Dorfman operad GD and the
Conformal Lie Operad CLie. The latter is the operad governing the Lie conformal
algebra structure. We prove Koszulity of the Conformal Lie operad using the
Groebner bases theory for operads and an operadic analogue of the Priddy
criterion. An example of deformation of an operad coming from the Hom
structures is considered. In particular we study possible deformations of the
Associative operad from the point of view of the confluence property. Only one
deformation, the operad which governs the identity turns out to be confluent. We introduce a new Hom structure, namely
Hom--Gelfand-Dorfman algebras and study their basic properties.Comment: 24 page
Relaxed multi category structure of a global category of rings and modules
In this paper we describe how to give a particular global category of rings
and modules the structure of a relaxed multi category, and we describe an
algebra in this relaxed multi category such that vertex algebras appear as such
algebras.Comment: 19 pages, xy-pic, epsfig. Updated version to appear in the Journal of
Pure and Applied Algebra including various corrections and additional
citation
Operads of compatible structures and weighted partitions
In this paper we describe operads encoding two different kinds of
compatibility of algebraic structures. We show that there exist decompositions
of these in terms of black and white products and we prove that they are Koszul
for a large class of algebraic structures by using the poset method of B.
Vallette. In particular we show that this is true for the operads of compatible
Lie, associative and pre-Lie algebras.Comment: 16 pages, main result about Koszulness generalized to a large class
of compatible structure
On a theorem of Kontsevich
In two seminal papers M. Kontsevich introduced graph homology as a tool to
compute the homology of three infinite dimensional Lie algebras, associated to
the three operads `commutative,' `associative' and `Lie.' We generalize his
theorem to all cyclic operads, in the process giving a more careful treatment
of the construction than in Kontsevich's original papers. We also give a more
explicit treatment of the isomorphisms of graph homologies with the homology of
moduli space and Out(F_r) outlined by Kontsevich. In [`Infinitesimal operations
on chain complexes of graphs', Mathematische Annalen, 327 (2003) 545-573] we
defined a Lie bracket and cobracket on the commutative graph complex, which was
extended in [James Conant, `Fusion and fission in graph complexes', Pac. J. 209
(2003), 219-230] to the case of all cyclic operads. These operations form a Lie
bi-algebra on a natural subcomplex. We show that in the associative and Lie
cases the subcomplex on which the bi-algebra structure exists carries all of
the homology, and we explain why the subcomplex in the commutative case does
not.Comment: Published by Algebraic and Geometric Topology at
http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-42.abs.htm
A General Framework for Sound and Complete Floyd-Hoare Logics
This paper presents an abstraction of Hoare logic to traced symmetric
monoidal categories, a very general framework for the theory of systems. Our
abstraction is based on a traced monoidal functor from an arbitrary traced
monoidal category into the category of pre-orders and monotone relations. We
give several examples of how our theory generalises usual Hoare logics (partial
correctness of while programs, partial correctness of pointer programs), and
provide some case studies on how it can be used to develop new Hoare logics
(run-time analysis of while programs and stream circuits).Comment: 27 page
Compositional uniformity, domain patterning and the mechanism underlying nano-chessboard arrays
We propose that systems exhibiting compositional patterning at the nanoscale,
so far assumed to be due to some kind of ordered phase segregation, can be
understood instead in terms of coherent, single phase ordering of minority
motifs, caused by some constrained drive for uniformity. The essential features
of this type of arrangements can be reproduced using a superspace construction
typical of uniformity-driven orderings, which only requires the knowledge of
the modulation vectors observed in the diffraction patterns. The idea is
discussed in terms of a simple two dimensional lattice-gas model that simulates
a binary system in which the dilution of the minority component is favored.
This simple model already exhibits a hierarchy of arrangements similar to the
experimentally observed nano-chessboard and nano-diamond patterns, which are
described as occupational modulated structures with two independent modulation
wave vectors and simple step-like occupation modulation functions.Comment: Preprint. 11 pages, 11 figure
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