45 research outputs found
Koszul duality in deformation quantization and Tamarkin's approach to Kontsevich formality
Let be a quadratic Poisson bivector on a vector space . Then one
can also consider as a quadratic Poisson bivector on the vector space
. Fixed a universal deformation quantization (prediction some weights
to all Kontsevich graphs [K97]), we have deformation quantization of the both
algebras and . These are graded quadratic algebras, and
therefore Koszul algebras. We prove that for some universal deformation
quantization, independent on , these two algebras are Koszul dual. We
characterize some deformation quantizations for which this theorem is true in
the framework of the Tamarkin's theory [T1].Comment: 49 pages, 2 figure
On L-infinity morphisms of cyclic chains
Recently the first two authors constructed an L-infinity morphism using the
S^1-equivariant version of the Poisson Sigma Model (PSM). Its role in
deformation quantization was not entirely clear. We give here a "good"
interpretation and show that the resulting formality statement is equivalent to
formality on cyclic chains as conjectured by Tsygan and proved recently by
several authors.Comment: 11 page
The Shapovalov determinant for the Poisson superalgebras
Among simple Z-graded Lie superalgebras of polynomial growth, there are
several which have no Cartan matrix but, nevertheless, have a quadratic even
Casimir element C_{2}: these are the Lie superalgebra k^L(1|6) of vector fields
on the (1|6)-dimensional supercircle preserving the contact form, and the
series: the finite dimensional Lie superalgebra sh(0|2k) of special Hamiltonian
fields in 2k odd indeterminates, and the Kac--Moody version of sh(0|2k). Using
C_{2} we compute N. Shapovalov determinant for k^L(1|6) and sh(0|2k), and for
the Poisson superalgebras po(0|2k) associated with sh(0|2k). A. Shapovalov
described irreducible finite dimensional representations of po(0|n) and
sh(0|n); we generalize his result for Verma modules: give criteria for
irreducibility of the Verma modules over po(0|2k) and sh(0|2k)
The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization
Using normal coordinates in a Poincar\'e-Birkhoff-Witt basis for the Hopf
algebra of renormalization in perturbative quantum field theory, we investigate
the relation between the twisted antipode axiom in that formalism, the Birkhoff
algebraic decomposition and the universal formula of Kontsevich for quantum
deformation.Comment: 21 pages, 15 figure
Клинико-функциональные нарушения сердечно-сосудистой системы у пациентов с хронической обструктивной болезнью легких при наличии хронической сердечной недостаточности
The study was aimed to investigate clinical and functional particularities of cardiovascular system in patients with COPD and chronic heart failure (CHF). We examined 1737 patients, of them, 498 with COPD (the 1st group), 721 with COPD and concomitant class I to III stable angina (the 2nd group), and 519 with class I to III stable angina (the 3rd group). All the patients also had CHF. The study included clinical assessment using modified R. Cody's scale, ECG, Holter monitoring, lung function testing, Doppler echocardiography, 6-minute walk test (6MWT). Obstructive disorders were found in 424 of the 2nd group patients (58.8 %) and 268 of the 3rd group patients (51.7 %). Number of patients with class II to IV chronic cor pulmonale was similar in all groups. The class III was determined more often in the 2nd group (36.5 %; р < 0.05), the class I prevailed in the 1st group (17.8 %; р < 0.05). The stage I CHF predominated in the 1st group (31.9 %; р < 0.05), the stages IIА and IIБ were seen mainly in the 2nd group (51.6 % and 26.4 % respectively; р < 0.05). The majority of the 3rd group patients (57.3 %) had the stage IIA CHF. According to most clinical signs, CHF was more severe in the 2nd group. 6MWT was 308.08 ± 6.03 m in the 1st group, 156.4 ± 4.38 m in the 2nd group, and 212.8 ± 5.65 m in the 3rd group (р < 0.05). Low left ventricular (LV) ejection fraction was seen significantly more often in COPD patients with concomitant angina. This group as well as COPD patients had significantly higher mean pulmonary artery pressure (mPAP) (24.7 ± 0.41 mm Hg and 29.9 ± 0.27 mm Hg respectively) compared to 21.7 ± 0.07 mm Hg in the 3rd group patients. Right ventricular (RV) diastolic dysfunction was revealed in 154 patients of the 1st group (83.7 %), 194 patients of the 2nd group (91.9 %) and 72 patients of the 3rd group (43.1 %). In conclusion, all the patients had RV and LV remodeling signs. COPD patients had more prominent RV hypertrophy and dilation, angina patients had enlargement of left heart and moderate decrease in LV contractility. The patients with COPD and angina had the greatest increase in size and wall thickness of both LV and RV and low pump function of LV.Целью исследования явилось изучение особенностей клинико-функциональных нарушений сердечно-сосудистой системы у больных ХОБЛ при наличии хронической сердечной недостаточности (ХСН). Обследовано 1 737 пациентов: 498 – с ХОБЛ (1-я группа), 721 с сочетанием ХОБЛ и стенокардии напряжения I–III функциональных классов (ФК) (2-я группа), 519 – со стенокардией напряжения I–III ФК (3-я группа). У всех больных ХСН проводили оценку клинического состояния по шкале R.Cody в модификации В.Ю.Мареева (ШОКС), ЭКГ, суточное мониторирование ЭКГ по Холтеру, функции внешнего дыхания, эходопплерокардиографию, тест с 6-минутной ходьбой (6-МШТ). Обструктивные нарушения легочной вентиляции разной степени выраженности имели 424 (58,8 %) больных 2-й группы и 268 (51,7 %) больных 3-й группы. Количество больных с хроническим легочным сердцем II и IV ФК было примерно одинаковым в группах. Больных с III ФК было больше во 2-й группе (36,5 %; р < 0,05), I ФК – в 1-й группе (17,8 %; р < 0,05). ХСН I стадии чаще выявлялась в 1-й группе (31,9 %; р < 0,05), IIА и IIБ стадий – во 2-й группе (51,6 и 26,4 % соответственно; р < 0,05). Более чем у1 / 2 пациентов 3-й группы (57,3 %) была диагностирована IIА стадия ХСН. По большинству клинических проявлений у больных 2-й группы ХСН была более тяжелой. Дистанция в 6-МШТ составила 308,08 ± 6,03 м в 1-й группе, 156,4 ± 4,38 м во 2-й группе и 212,8 ± 5,65 м в 3й группе (р < 0,05). У больных с сочетанием ХОБЛ и ишемической болезни сердца (ИБС) низкая фракция выброса левого желудочка (ЛЖ) выявлялась достоверно чаще. В группах больных ХОБЛ и с сочетанием ХОБЛ и ИБС среднее давление в легочной артерии (СрДЛА) было значимо выше (24,7 ± 0,41 и 29,9 ± 0,27 мм рт. ст. соответственно) по сравнению с 21,7 ± 0,07 мм рт. ст. в 3-й группе. Диастолическая дисфункция правого желудочка (ПЖ) выявлена у 154 (83,7 %) больных 1-й группы, 194 (91,9 %) больных 2-й группы и 72 (43,1 %) больных 3-й группы. Таким образом, у больных всех групп наблюдались процессы ремоделирования ЛЖ и ПЖ. У пациентов с ХОБЛ были более выражены признаки гипертрофии и дилатации ПЖ, у больных ИБС – увеличение левых отделов сердца, а также некоторое снижение показателей сократимости ЛЖ, при сочетании ХОБЛ и ИБС наиболее выраженным было увеличение размеров и толщины стенок обоих желудочков и снижение насосной функции ЛЖ
M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra
We show that the zeroth cohomology of M. Kontsevich's graph complex is
isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is
explicitly described. This result has applications to deformation quantization
and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber
operad. They are parameterized by grt_1, up to one class (or two, depending on
the definitions). More generally, the homotopy derivations of the (non-unital)
E_n operads may be expressed through the cohomology of a suitable graph
complex. Our methods also give a second proof of a result of H. Furusho,
stating that the pentagon equation for grt_1-elements implies the hexagon
equation
Symmetry, Gravity and Noncommutativity
We review some aspects of the implementation of spacetime symmetries in
noncommutative field theories, emphasizing their origin in string theory and
how they may be used to construct theories of gravitation. The geometry of
canonical noncommutative gauge transformations is analysed in detail and it is
shown how noncommutative Yang-Mills theory can be related to a gravity theory.
The construction of twisted spacetime symmetries and their role in constructing
a noncommutative extension of general relativity is described. We also analyse
certain generic features of noncommutative gauge theories on D-branes in curved
spaces, treating several explicit examples of superstring backgrounds.Comment: 52 pages; Invited review article to be published in Classical and
Quantum Gravity; v2: references adde
Effective Batalin--Vilkovisky theories, equivariant configuration spaces and cyclic chains
Kontsevich's formality theorem states that the differential graded Lie
algebra of multidifferential operators on a manifold M is
L-infinity-quasi-isomorphic to its cohomology. The construction of the
L-infinity map is given in terms of integrals of differential forms on
configuration spaces of points in the upper half-plane. Here we consider
configuration spaces of points in the disk and work equivariantly with respect
to the rotation group. This leads to considering the differential graded Lie
algebra of multivector fields endowed with a divergence operator. In the case
of R^d with standard volume form, we obtain an L-infinity morphism of modules
over this differential graded Lie algebra from cyclic chains of the algebra of
functions to multivector fields. As a first application we give a construction
of traces on algebras of functions with star-products associated with
unimodular Poisson structures. The construction is based on the
Batalin--Vilkovisky quantization of the Poisson sigma model on the disk and in
particular on the treatment of its zero modes.Comment: 27 page