Search results for " Conformal"
showing 10 items of 51 documents
Lie Algebras Generated by Extremal Elements
1999
We study Lie algebras generated by extremal elements (i.e., elements spanning inner ideals of L) over a field of characteristic distinct from 2. We prove that any Lie algebra generated by a finite number of extremal elements is finite dimensional. The minimal number of extremal generators for the Lie algebras of type An, Bn (n>2), Cn (n>1), Dn (n>3), En (n=6,7,8), F4 and G2 are shown to be n+1, n+1, 2n, n, 5, 5, and 4 in the respective cases. These results are related to group theoretic ones for the corresponding Chevalley groups.
Stereotactic fractionated irradiation of optic nerve sheath meningioma: a new treatment alternative
2002
Background: Primary optic nerve sheath meningioma (ONSM) is a rare but almost invariably blinding tumour when its natural history is observed in a “wait and see” strategy. Surgery has hitherto only been advocated in case of progressive disease involving intracranial structures, as it leads to iatrogenic blindness in the overwhelming majority of cases. Therefore, treatment options bearing lesser risk of functional deterioration are highly desirable, both in cases of intracranial involvement as well as during earlier phases of the disease which are currently generally left untreated. The authors report the outcome of the largest series of patients to date treated by stereotactic fractionated …
The Potential Role of Lung Ultrasound B-Lines for Detection of Lung Radio-Induced Toxicity in Breast Cancer Patients after Radiation Therapy.
2016
Breast cancer patients exposed to doses of radiation after radiotherapy could develop toxicity to lung. Lung ultrasound (LUS) is able to detect interstitial lung disease by the evaluation of B-lines. The aim of our study was to assess the number of B-lines to diagnose lung involvement after chest radiotherapy.We measured LUS B-lines in the treated and contralateral lung of 20 breast cancer patients, 1-3 months after the end of radiotherapy and 1 year after previous LUS. The sum of the B-lines number in the 72 sites on anterior and posterior chest yielded a global B-lines score.B-lines were more numerous in treated (median: 21; 1st-3rd quartiles: 11-31) versus untreated hemithorax (median: 3…
The enveloping algebra of the Lie superalgebra osp(1,2)
1990
International audience
Star-products and phase space realizations of quantum groups
1992
It is shown for a family of *-products (i.e. different ordering rules) that, under a strong invariance condition, the functions of the quadratic preferred observables (which generate the Cartan subalgebra in phase space realization of Lie algebras) take only the linear or exponential form. An exception occurs for the case of a symmetric ordering *-product where trigonometric functions and two special polynomials can also be included. As an example, the ‘quantized algebra’ of the oscillator Lie algebra is argued.
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.
Primary optic nerve sheath meningioma
2007
BACKGROUND. Radiotherapy (RT) has occasionally been practiced in the treatment of optic nerve sheath meningioma (ONSM). Recently, stereotactic fractionated RT (SFRT) has been introduced as a tool with better precision for RT delivery. A comprehensive review was undertaken to provide more insight into this matter. METHODS. A literature search was performed to identify reports dealing with both clinical aspects (diagnosis) and treatment in ONSM, focusing on RT in primary (p)ONSM. In particular, major emphasis was placed on the role of SFRT in pONSM. RESULTS. SFRT was capable of achieving excellent local tumor control, with improved/stable functional capacity in ≥80%, accompanied with very low…
Semisimple Lie Algebras
1989
Let F be the field of real or complex numbers. A Lie algebra is a vector space g over F with a Lie product (or commutator) [·,·]: g × g → g such that $$x \mapsto \left[ {x,y} \right]\;is\;linear\;for\;any\;y \in g,$$ (1) $$\left[ {x,y} \right] =- \left[ {y,x} \right],$$ (2) $$\left[ {x,\left[ {y,z} \right]} \right] + \left[ {y,\left[ {z,x} \right]} \right] + \left[ {z,\left[ {x,y} \right]} \right] = 0.$$ (3) The last condition is called the Jacobi identity. From (1) and (2) it follows that also y ↦ [x,y] is linear for any x ∈ g. In this chapter we shall consider only fini te-dimensional Lie algebras. In any vector space g one can always define a trivial Lie product [x,y] = 0. A Lie algebra …
Indecomposable modules over the Virasoro Lie algebra and a conjecture of V. Kac
1991
We consider a class of indecomposable modules over the Virasoro Lie algebra that we call bounded admissible modules. We get results concerning the center and the dimensions of the weight spaces. We prove that these modules always contain a submodule with one-dimensional weight spaces. From this follows the proof of a conjecture of V. Kac concerning the classification of simple admissible modules.
Non-integrality of the PI-exponent of special Lie algebras
2013
If L is a special Lie algebra over a field of characteristic zero, its sequence of codimensions is exponentially bounded. The PI-exponent measures the exponential rate of growth of such sequence and here we give a first example of a special Lie algebra whose (upper and lower) PI-exponent is non-integer.