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Two theorems involving curl eigenfields on the 3--sphere are obtained using angular momentum theory. Spinor hyperspherical harmonics are shown to form an explicit, convenient basis. In particular, a spin--one vector calculus is reviewed. An…

Differential Geometry · Mathematics 2023-05-09 J. S. Dowker

This work offers an extension of the deformation procedure introduced in field theory to the case of standard cosmology in the presence of real scalar field in flat space-time. The procedure is shown to work for many models, which give rise…

Astrophysics · Physics 2024-02-23 Dionisio Bazeia , Laercio Losano , Alan B. Pavan

In this article, we use Harrison cohomology to provide a framework for commutative deformations. In particular, Kontsevich's result that formality of (the Hochschild complex of) an associative algebra implies its deformability is adapted…

Quantum Algebra · Mathematics 2017-02-28 Olivier Elchinger

The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Lie conformal superalgebras. Firstly, we construct the semidirect product of a Lie conformal superalgebra and…

Rings and Algebras · Mathematics 2017-11-23 Jun Zhao , Liangyun Chen , Lamei Yuan

This is the third paper in a series. In part I we developed a deformation theory of objects in homotopy and derived categories of DG categories. Here we show how this theory can be used to study deformations of objects in homotopy and…

Algebraic Geometry · Mathematics 2018-08-13 Alexander I. Efimov , Valery A. Lunts , Dmitri O. Orlov

We provide further techniques to study the Dolbeault and Bott-Chern cohomologies of deformations of solvmanifolds by means of finite-dimensional complexes. By these techniques, we can compute the Dolbeault and Bott-Chern cohomologies of…

Complex Variables · Mathematics 2017-05-15 Daniele Angella , Hisashi Kasuya

We know that coalgebra measurings behave like generalized maps between algebras. In this note, we show that coalgebra measurings between commutative algebras induce morphisms between higher order Hochschild homology groups of algebras. By…

Rings and Algebras · Mathematics 2025-04-10 Abhishek Banerjee , Surjeet Kour

Deformation theory can be used to compute the cohomology of a deformed algebra with coefficients in itself from that of the original. Using the invariance of the Euler-Poincare characteristic under deformation, it is applied here to compute…

Quantum Algebra · Mathematics 2012-08-03 Murray Gerstenhaber , Anthony Giaquinto

In this paper we present a three-dimensional discrete model governing the deformation of a viral capsid, modelled as a regular icosahedron and subjected not to cross a given flat rigid surface on which it initially lies in correspondence of…

Analysis of PDEs · Mathematics 2022-04-15 Paolo Piersanti , Kristen White , Bogdan Dragnea , Roger Temam

Quantum Drinfeld Hecke algebras are generalizations of Drinfeld Hecke algebras in which polynomial rings are replaced by quantum polynomial rings. We identify these algebras as deformations of skew group algebras, giving an explicit…

Rings and Algebras · Mathematics 2014-01-07 Deepak Naidu , Sarah Witherspoon

We use a Heegaard splitting of the topological 3-sphere as a guiding principle to construct a family of its noncommutative deformations. The main technical point is an identification of the universal C*-algebras defining our quantum…

K-Theory and Homology · Mathematics 2009-09-29 Paul Baum , Piotr M. Hajac , Rainer Matthes , Wojciech Szymanski

The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and…

Rings and Algebras · Mathematics 2017-11-23 Jun Zhao , Lamei Yuan , Liangyun Chen

When can a map between manifolds be deformed away from itself? We describe a (normal bordism) obstruction which is often computable and in general much stronger than the classical primary obstruction in cohomology. In particular, it answers…

Algebraic Topology · Mathematics 2007-05-23 Ulrich Koschorke

We construct a collection of higher Chow cycles on certain surfaces which degenerate to an arrangement of planes in general position. When its degree is 4, this construction gives a new explicit proof of the Hodge-D-Conjecture for a certain…

Algebraic Geometry · Mathematics 2021-06-08 Tokio Sasaki

In this work we define a deformation theory for the Coupled K\"ahler-Yang-Mills equations in arXiv:1102.0991, generalizing work of Sz\'ekelyhidi on constant scalar curvature K\"ahler metrics. We use the theory to find new solutions of the…

Differential Geometry · Mathematics 2017-05-17 Mario Garcia-Fernandez , Carl Tipler

Hochschild cohomology governs deformations of algebras, and its graded Lie structure plays a vital role. We study this structure for the Hochschild cohomology of the skew group algebra formed by a finite group acting on an algebra by…

Rings and Algebras · Mathematics 2011-09-06 Anne V. Shepler , Sarah Witherspoon

We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more…

Quantum Algebra · Mathematics 2018-07-10 Martin Bordemann , Olivier Elchinger , Simone Gutt , Abdenacer Makhlouf

We discuss a relation between deformed cohomologies of symmetry pseudo-groups and coverings of differential equations. Examples include the potential Khokhlov--Zabolotskaya equation and the Boyer--Finley equation.

Differential Geometry · Mathematics 2015-11-10 Oleg I. Morozov

We reproduce the quantum cohomology of toric varieties (and of some hypersurfaces in projective spaces) as the cohomology of certain vertex algebras with differential. The deformation technique allows us to compute the cohomology of the…

Algebraic Geometry · Mathematics 2007-05-23 F. Malikov , V. Schechtman

We give a complete classification of the spherical 3-manifolds that bound smooth rational homology 4-balls. Furthermore, we determine the order of spherical 3-manifolds in the rational homology cobordism group of rational homology…

Geometric Topology · Mathematics 2019-10-17 Dong Heon Choe , Kyungbae Park