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Saturday, July 25, 2020 | History

3 edition of Deformation theory of algebras and structures and applications found in the catalog.

Deformation theory of algebras and structures and applications

NATO Advanced Study Institute on Deformation Theory of Algebras and Structures and Applications (1986 Castelvecchio Pascoli, Italy)

# Deformation theory of algebras and structures and applications

## by NATO Advanced Study Institute on Deformation Theory of Algebras and Structures and Applications (1986 Castelvecchio Pascoli, Italy)

Written in English

Subjects:
• Homotopy theory -- Congresses.,
• Perturbation (Mathematics) -- Congresses.,
• Algebra.

• Edition Notes

Classifications The Physical Object Statement edited by Michiel Hazewinkel and Murray Gerstenhaber. Series NATO ASI series. Series C, Mathematical and physical sciences ;, vol. 247, NATO ASI series., no. 247. Contributions Hazewinkel, Michiel., Gerstenhaber, Murray, 1927- LC Classifications QA612.7 .N38 1986 Pagination viii, 1030 p. : Number of Pages 1030 Open Library OL2049840M ISBN 10 9027728046 LC Control Number 88027389

This book is a survey of the theory of formal deformation quantization of Poisson manifolds, in the formalism developed by Kontsevich. It is intended as an educational introduction for mathematical physicists who are dealing with the subject for the first time. The main topics covered are theBrand: Springer International Publishing. This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics.

This thesis mainly studies deformation theories and applications of the operators on Lie algebras,Leibniz algebras and 3-Lie consists of six Chapter 1,we introduce the background and its recent development and analyzes the motivations and the main results of this Chapter 2,we present some basic notations. These algebras nowadays play an important rôle in many different areas, in particular via deformation theory. A very efficient tool to build such algebras is the derived bracket construction of T. Voronov. In this talk we will give a geometric interpretation of this construction and if time permits some applications of this new point of view.

Deformation theory and differential graded Lie algebras. Ask Question Asked 10 years, 7 months ago. Non-symmetric operads have the natural structure of a pre-Lie algebra, the composition is defined by taking the sum of all possible ways of plugging one operation into another. then the theory above is the deformation theory for O algebras.   In this section, we compare deformations and contractions of complex and real three-dimensional Lie algebras. Hereafter, the deformations of real three-dimensional Lie algebras are classified for the first time by using the recent deformation classification of the corresponding complex Lie algebras [ 15 ].Cited by:

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### Deformation theory of algebras and structures and applications by NATO Advanced Study Institute on Deformation Theory of Algebras and Structures and Applications (1986 Castelvecchio Pascoli, Italy) Download PDF EPUB FB2

This volume is a result of a meeting which took place in June at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer : Hardcover.

About this book. This volume is a result of a meeting which took place in June at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school.

Introduction. This volume is a result of a meeting which took place in June at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is perhaps desirable for a volume resulting from a summer school. In return it contains a good many results which were not yet available at the time of the meeting.

Deformation Theory of Algebras and Structures and Applications NATO ASI Series Advanced Science Institutes Series A Series presentmg the results of activities sponsored by the NA TO Science Committee, which aims at the dissemination of advanced scientific and technological knowledge, with a view to strengthening links between scientific communities.

Then, the physicists E. Inonu and E.P. Wigner introduced in the concept of "deformation of a Lie algebra" by considering the speed of light as Deformation theory of algebras and structures and applications book parameter in the Lorentz composition of speeds.

This idea led to the "deformation theory of algebraic structures" and the first applications of computer by: 4. Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry.

This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics. Deformation Theory of Algebras and Their Diagrams Title (HTML): Deformation Theory of Algebras and Their Diagrams This book brings together both the classical and current aspects of deformation theory.

The presentation is mostly self-contained, assuming only basic knowledge of commutative algebra, homological algebra and category theory. Algebraic deformation theory was -introduced for associative algebras by Ger- stenhaber [14], and was extended to Lie algebras by Nijenhuis and Richardson [23,24].

Their work closely parallels the theory of deformations of complex analytic structures, initiated by Kodaira and Spencer [21]. The fundamentalFile Size: 2MB. Algebraic deformation theory is primarily concerned with the interplay between homological algebra and the perturbations of algebraic structures.

We here offer a self-contained introduction to the subject, first describing the classical theory of deformations of associative algebras, then passing to the general case of algebras, coalgebras, and bialgebras defined by triples and by: Organized in the four areas of algebra, geometry, dynamical symmetries and conservation laws and mathematical physics and applications, the book covers deformation theory and quantization; Hom-algebras and n-ary algebraic structures; Hopf algebra, integrable systems and related math structures; jet theory and Weil bundles; Lie theory and.

A foundation for PROPs, algebras, and modules. formalism of polynomial monads allows recover various structures studied in the present book.

the first step to develop a unified treatment of deformation theory and obstruction theory of algebras over ­props with potential applications in the various situations where such structures occur.

In answer to your last paragraph, a good starting point for deformation theory, not specifically of quantum groups, is the first order deformation theory of associative algebras. algebra in a precise sense. Deformation theory started with the seminal work of Kodaira and Spencer [31] on deforma-tion of holomorphic manifolds and then expanded to the realm of algebraic geometry [28]; more recently it found striking applications in number theory [38].

At the same time, the idea of a Cited by: 1. DEFORMATION THEORY OF INFINITY ALGEBRAS ALICE FIALOWSKI AND MICHAEL PENKAVA Abstract. This work explores the deformation theory of alge-braic structures in a very general setting. These structures include commutative, associative algebras, Lie algebras, and the inﬁnity versions of these structures, the strongly homotopy associative and Lie.

In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered $$A_\infty$$ algebras and $$A_\infty$$ bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented.

Applications of deformation theory Bend-and-break. Deformation theory was famously applied in birational geometry by Shigefumi Mori to study the existence of rational curves on varieties.

For a Fano variety of positive dimension Mori showed that there is a rational curve passing through every point. Book Description. Noncommutative Deformation Theory is aimed at mathematicians and physicists studying the local structure of moduli spaces in algebraic geometry.

This book introduces a general theory of noncommutative deformations, with applications to the study of moduli spaces of representations of associative algebras and to quantum theory in physics. Define sL # Der h to be the d.g. Lie semi-direct product of the abelian d.g. Lie algebra sL with Der h which acts on sL in the obvious way: [Sf,01=S(f) The Lie algebra structure of tangent cohomology and deformation theory while d(sf)= =sdf+adf where ad f is the coderivation of T defined by the composite I'~I'QI'foI k0I'= by: In this chapter we present a second application of Poisson structures: the theory of deformations of commutative associative algebras, also called deformation quantization.

NATO Advanced Study Institute on Deformation Theory of Algebras and Structures and Applications ( Castelvecchio Pascoli, Italy). Deformation theory of algebras and structures and applications.

Dordrecht ; Boston: Kluwer, (OCoLC) Material Type: Conference publication, Internet resource: Document Type: Book, Internet Resource. Get this from a library! Deformation Theory of Algebras and Structures and Applications.

[Michiel Hazewinkel; Murray Gerstenhaber] -- This volume is a result of a meeting which took place in June at 'll Ciocco" in Italy entitled 'Deformation theory of algebras and structures and applications'. It appears somewhat later than is.In this paper we consider the deformation theory of di erential graded modules (DGM’s) and di erential graded algebras (DGA’s), where only the di erential varies, the underlying module or algebra structure remaining xed.

At the outset we consider only individual modules or algebras and afterwards we examine deformations of sheaves. In most File Size: KB. : An example of formal deformations of Lie algebras, “NATO Conference on deformation theory of algebras and applications, Proceedings”, Kluwer, Dordrecht () – 6.

Fialowski, A. and Fuchs, D.: Construction of miniversal Deformations of Lie Algebras, Journal of Functional Analysis (), 76 – Cited by: