Search results for "filtered"

Group graded algebras and almost polynomial growth

2011

Let F be a field of characteristic 0, G a finite abelian group and A a G-graded algebra. We prove that A generates a variety of G-graded algebras of almost polynomial growth if and only if A has the same graded identities as one of the following algebras: (1) FCp, the group algebra of a cyclic group of order p, where p is a prime number and p||G|; (2) UT2G(F), the algebra of 2×2 upper triangular matrices over F endowed with an elementary G-grading; (3) E, the infinite dimensional Grassmann algebra with trivial G-grading; (4) in case 2||G|, EZ2, the Grassmann algebra with canonical Z2-grading.

A note on cocharacter sequence of Jordan upper triangular matrix algebra

2016

Let UJn(F) be the Jordan algebra of n × n upper triangular matrices over a field F of characteristic zero. This paper is devoted to the study of polynomial identities satisfied by UJ2(F) and UJ3(F). In particular, the goal is twofold. On one hand, we complete the description of G-graded polynomial identities of UJ2(F), where G is a finite abelian group. On the other hand, we compute the Gelfand–Kirillov dimension of the relatively free algebra of UJ2(F) and we give a bound for the Gelfand–Kirillov dimension of the relatively free algebra of UJ3(F).

The new results on lattice deformation of current algebra

2008

The topic “Quantum Integrable Models” was reviewed in the literature and presented to the conferences and schools many times. Only the reports of our own have been done on quite a few occasions (see, e.g., [1], [2]). So here we shall try to present a fresh approach to the description of the ingredients of construction of integrable models. It has gradually evolved in the process of our joint work. Whereas our goal was the Sugawara construction for the lattice affine algebra (known now as the St.Petersburg algebra), (see, e.g., [1]), some technical developments happen to be new and useful for the already developed subjects. Here we shall underline this development.

Sturmian words and overexponential codimension growth

2018

Abstract Let A be a non necessarily associative algebra over a field of characteristic zero satisfying a non-trivial polynomial identity. If A is a finite dimensional algebra or an associative algebra, it is known that the sequence c n ( A ) , n = 1 , 2 , … , of codimensions of A is exponentially bounded. If A is an infinite dimensional non associative algebra such sequence can have overexponential growth. Such phenomenon is present also in the case of Lie or Jordan algebras. In all known examples the smallest overexponential growth of c n ( A ) is ( n ! ) 1 2 . Here we construct a family of algebras whose codimension sequence grows like ( n ! ) α , for any real number α with 0 α 1 .

POLYNOMIAL GROWTH OF THE*-CODIMENSIONS AND YOUNG DIAGRAMS

2001

Let A be an algebra with involution * over a field F of characteristic zero and Id(A, *) the ideal of the free algebra with involution of *-identities of A. By means of the representation theory of the hyperoctahedral group Z 2wrS n we give a characterization of Id(A, *) in case the sequence of its *-codimensions is polynomially bounded. We also exhibit an algebra G 2 with the following distinguished property: the sequence of *-codimensions of Id(G 2, *) is not polynomially bounded but the *-codimensions of any T-ideal U properly containing Id(G 2, *) are polynomially bounded.

Group-graded algebras with polynomial identity

1998

LetG be a finite group and letR=Σg∈GRg be any associative algebra over a field such that the subspacesRg satisfyRgRh⊆Rgh. We prove that ifR1 satisfies a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the order ofG. This result implies the following: ifH is a finite-dimensional semisimple commutative Hopfalgebra andR is anyH-module algebra withRH satisfying a PI of degreed, thenR satisfies a PI of degree bounded by an explicit function ofd and the dimension ofH.

Probing Physical Properties of Confined Fluids within Individual Nanobubbles

2008

Spatially resolved electron energy-loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM) has been used to investigate as fluidic phase in nanoubbles embedded in a metallic Pd90Pt10 matrix. Using the 1s->2p excitation of the He atoms, maps of the He distribution, in particular of its density an pressure in bubbles of different diameter have been realized, thus providing an indication of the involved bubble formation mechanism. However, the short-range Pauli repulsion mechanism between electrons on neighboring atoms seems insufficient to interpret minute variations of the local local measurements performed at the interface between the metal and the He bubble. Simul…

A Scanning Electron Microscope for Ultracold Atoms

2006

We propose a new technique for the detection of single atoms in ultracold quantum gases. The technique is based on scanning electron microscopy and employs the electron impact ionization of trapped atoms with a focussed electron probe. Subsequent detection of the resulting ions allows for the reconstruction of the atoms position. This technique is expected to achieve a much better spatial resolution compared to any optical detection method. In combination with the sensitivity to single atoms, it makes new in situ measurements of atomic correlations possible. The detection principle is also well suited for the addressing of individual sites in optical lattices.

1996

The uses of atomic force microscopy, scanning tunneling microscopy, electron spectroscopic imaging, electron energy loss spectroscopy and low voltage, high resolution scanning electron microscopy in polymer research are reviewed

On the 1-handles of the product V3XBn for a simply connected open 3-manifold V3

2013

Although \pi_1^\inftyV^3 is an obstruction for killing stably the 1-handles of an open simply connected 3-manifold V^3, one can always get rid of the 1-handles of V^3\times B^n, for high enough n, at price of a certain nonmetrizable slackening of the topology.