相关论文: Chiral Splitting at Work
Proper group actions are ubiquitous in mathematics and have many of the attractive features of actions of compact groups. In this survey, we discuss proper actions of Lie groups on smooth manifolds. If the group dimension is sufficiently…
Many two-dimensional classical field theories have hidden symmetries that form an infinite-dimensional algebra. For those examples that correspond to effective descriptions of compactified superstring theories, the duality group is expected…
In this survey we discuss a wide variety of aspects related to Lie group integrators. These numerical integration schemes for differential equations on manifolds have been studied in a general and systematic manner since the 1990s and the…
We present two versions of the Egorov theorem for orbifolds. The first one is a straightforward extension of the classical theorem for smooth manifolds. The second one considers an orbifold as a singular manifold, the orbit space of a Lie…
A new, second-order solution in curvilinear coordinates is introduced for the relative motion of two spacecraft on eccentric orbits. The second-order equations for unperturbed orbits are derived in spherical coordinates with true anomaly as…
In this paper, we study partial actions of groups on $R$-algebras, where $R$ is a commutative ring. We describe the partial actions of groups on the indecomposable algebras with enveloping actions. Then we work on algebras that can be…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
This is the first of two papers which aim to understand quasi-isometries of a subclass of unimodular split solvable Lie groups. In the present paper, we show that locally (in a coarse sense), a quasi-isometry between two groups in this…
Chiral algebras in the cohomology of the $\overline{Q}_+$ supercharge of two-dimensional $\mathcal{N}=(0,2)$ theories on flat spacetime are discussed. Using the supercurrent multiplet, we show that the answer is renormalization group…
This paper is concerned with difference equations on elliptic curves. We establish some general properties of the difference Galois groups of equations of order two, and give applications to the calculation of some difference Galois groups.…
Magnons in antiferromagnets exhibit two chiral modes, providing an intrinsic degree of freedom for magnon-based computing architectures and spintronic devices. Electrical control of chiral splitting is crucial for applications, but remains…
We generate by computer a basis of invariants for the fundamental representations of the exceptional Lie groups E(6) and E(7), up to degree 18. We discuss the relevance of this calculation for the study of supersymmetric gauge theories, and…
In this paper, we study spinor Frenet equations in three dimensional Lie Groups with a bi-invariant metric. Also, we obtain spinor Frenet equations for special cases of three dimensional Lie groups.
We establish a link between the study of completely integrable systems of partial differential equations and the study of generic submanifolds in C^n. Using the recent developments of Cauchy-Riemann geometry we provide the set of symmetries…
We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.
In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of $b$-symplectic manifolds started in [12], we prove a slice theorem for Lie group actions on $b$-symplectic manifolds.
Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.
We explain that general differential calculus and Lie theory have a common foundation: Lie Calculus is differential calculus, seen from the point of view of Lie theory, by making use of the groupoid concept as link between them. Higher…
A survey of some results and open questions related to the following algebraic invariants of compact complex manifolds, that can be obtained from differential forms: cohomology groups, Chern classes, rational homotopy groups, and higher…
In this book, I explored differential equations for operation in Lie group and for representations of group Lie in a vector space.