171 research outputs found
Composition-Diamond lemma for -differential associative algebras with multiple operators
In this paper, we establish the Composition-Diamond lemma for
-differential associative algebras over a field with multiple
operators. As applications, we obtain Gr\"{o}bner-Shirshov bases of free
-differential Rota-Baxter algebras. In particular, linear bases of
free -differential Rota-Baxter algebras are obtained and consequently,
the free -differential Rota-Baxter algebras are constructed by words
Conformal invariance in 2-dimensional discrete field theory
A discretized massless wave equation in two dimensions, on an appropriately
chosen square lattice, exactly reproduces the solutions of the corresponding
continuous equations. We show that the reason for this exact solution property
is the discrete analog of conformal invariance present in the model, and find
more general field theories on a two-dimensional lattice that exactly solve
their continuous limit equations. These theories describe in general
non-linearly coupled bosonic and fermionic fields and are similar to the
Wess-Zumino-Witten model.Comment: 18 pages, RevTeX, 2 figures included; revision of title and
introductio
Soliton-potential interaction in the nonlinear Klein-Gordon model
The interaction of solitons with external potentials in nonlinear
Klein-Gordon field theory is investigated using an improved model. The
presented model has been constructed with a better approximation for adding the
potential to the Lagrangian through the metric of background space-time. The
results of the model are compared with another model and the differences are
discussed.Comment: 14 pages,8 figure
Multi-operator brackets acting thrice
We generalize an identity, first found by Bremner, for the action of three
nested Nambu brackets.Comment: Added references and detailed proof of main result, conforming to
journal versio
Functions of several Cayley-Dickson variables and manifolds over them
Functions of several octonion variables are investigated and integral
representation theorems for them are proved. With the help of them solutions of
the -equations are studied. More generally functions of
several Cayley-Dickson variables are considered. Integral formulas of the
Martinelli-Bochner, Leray, Koppelman type used in complex analysis here are
proved in the new generalized form for functions of Cayley-Dickson variables
instead of complex. Moreover, analogs of Stein manifolds over Cayley-Dickson
graded algebras are defined and investigated
Topics on n-ary algebras
We describe the basic properties of two n-ary algebras, the Generalized Lie
Algebras (GLAs) and, particularly, the Filippov (or n-Lie) algebras (FAs), and
comment on their n-ary Poisson counterparts, the Generalized Poisson (GP) and
Nambu-Poisson (N-P) structures. We describe the Filippov algebra cohomology
relevant for the central extensions and infinitesimal deformations of FAs. It
is seen that semisimple FAs do not admit central extensions and, moreover, that
they are rigid. This extends the familiar Whitehead's lemma to all
FAs, n=2 being the standard Lie algebra case. When the n-bracket of the FAs is
no longer required to be fully skewsymmetric one is led to the n-Leibniz (or
Loday's) algebra structure. Using that FAs are a particular case of n-Leibniz
algebras, those with an anticommutative n-bracket, we study the class of
n-Leibniz deformations of simple FAs that retain the skewsymmetry for the first
n-1 entires of the n-Leibniz bracket.Comment: 11 page
Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables
This paper is devoted to the specific class of pseudoconformal mappings of
quaternion and octonion variables. Normal families of functions are defined and
investigated. Four criteria of a family being normal are proven. Then groups of
pseudoconformal diffeomorphisms of quaternion and octonion manifolds are
investigated. It is proven, that they are finite dimensional Lie groups for
compact manifolds. Their examples are given. Many charactersitic features are
found in comparison with commutative geometry over or .Comment: 55 pages, 53 reference
On Deformations of n-Lie algebras
The aim of this paper is to review the deformation theory of -Lie
algebras. We summarize the 1-parameter formal deformation theory and provide a
generalized approach using any unital commutative associative algebra as a
deformation base. Moreover, we discuss degenerations and quantization of
-Lie algebras.Comment: Proceeding of the conference Dakar's Workshop in honor of Pr Amin
Kaidi. arXiv admin note: text overlap with arXiv:hep-th/9602016 by other
author
Sufficient conditions for the convergence of the Magnus expansion
Two different sufficient conditions are given for the convergence of the
Magnus expansion arising in the study of the linear differential equation . The first one provides a bound on the convergence domain based on the
norm of the operator . The second condition links the convergence of the
expansion with the structure of the spectrum of , thus yielding a more
precise characterization. Several examples are proposed to illustrate the main
issues involved and the information on the convergence domain provided by both
conditions.Comment: 20 page
Magnetic and Electronic Properties of Metal-Atom Adsorbed Graphene
We systematically investigate the magnetic and electronic properties of
graphene adsorbed with diluted 3d-transition and noble metal atoms using first
principles calculation methods. We find that most transition metal atoms (i.e.
Sc, Ti, V, Mn, Fe) favor the hollow adsorption site, and the interaction
between magnetic adatoms and \pi-orbital of graphene induces sizable exchange
field and Rashba spin-orbit coupling, which together open a nontrivial bulk gap
near the Dirac points leading to the quantum-anomalous Hall effect. We also
find that the noble metal atoms (i.e. Cu, Ag, Au) prefer the top adsorption
site, and the dominant inequality of the AB sublattice potential opens another
kind of nontrivial bulk gap exhibiting the quantum-valley Hall effect.Comment: Submitted to PRL on Aug. 10, 2011. 11 pages(4.5 pages for the main
text and 6.5 pages for the supporting materials
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