Related papers: On Complex Manifolds and Observable Schemes
We introduce a class of maps from an affine flat into a Riemannian manifold that solve an elliptic system defined by the natural second order elliptic operator of the affine structure and the nonlinear Riemann geometry of the target. These…
A technique to simulate the spex-mixer/mill system as a macroscopic ensemble rather than a pure dynamical system is proposed. The treatment is suitable especially for comminution processes generating the nanomaterial up to nanometers scale…
We provide a new method for constructing equiangular tight frames (ETFs). The construction is valid in both the real and complex settings, and shows that many of the few previously-known examples of ETFs are but the first representatives of…
Explicit structure constants are calculated for certain Lie algebras of vectorfields on 2-dimensional compact manifolds.
The use of geometric invariants has recently played an important role in the solution of classification problems in non-commutative ring theory. We construct geometric invariants of non-commutative projectivizations, a significant class of…
We examine several algebraic properties of the noncommutive $z$-plane and Riemann surfaces. The starting point of our investigation is a two-dimensional noncommutative field theory, and the framework of the theory will be converted into…
Using some elementary methods from noncommutative geometry a structure is given to a point of space-time which is different from and simpler than that which would come from extra dimensions. The structure is described by a supplementary…
We develop a homotopical variant of the classic notion of an algebraic theory as a tool for producing deformations of homotopy theories. From this, we extract a framework for constructing and reasoning with obstruction theories and spectral…
We investigate complex structures on the Oeljeklaus-Toma manifolds. The Oeljeklaus-Toma manifolds are defined using complex embeddings of number fields. By replacing these embeddings with their conjugates, one obtains other manifolds that…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions…
This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the…
In the construction of spectral manifolds in noncommutative geometry, a higher degree Heisenberg commutation relation involving the Dirac operator and the Feynman slash of real scalar fields naturally appears and implies, by equality with…
New splitting theorems in a semi-Riemannian manifold which admits an irrotational vector field (not necessarily a gradient) with some suitable properties are obtained. According to the extras hypothesis assumed on the vector field, we can…
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…
Following the B. Hiley belief that unresolved problems of conventional quantum mechanics could be the result of a wrong mathematical structure, an alternative basic structure is suggested. Critical part of the structure is modification of…
We develop a method to construct elusive functions using techniques of commutative algebra and algebraic geometry. The key notions of this method are elusive subsets and evaluation mappings. We also develop the effective elimination theory…
Let $X$ be a scheme. In this text, we extend the known definitions of a topology on the set $X(R)$ of $R$-rational points from topological fields, local rings and ad\`ele rings to any ring $R$ with a topology. This definition is functorial…
Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.
We conjecture an algorithm to construct spin multipartitions and prove that all the level one Fock spaces using our combinatorics are modules over the quantum enveloping algebra.
A covariant functor from the category of generic complex algebraic curves to a category of the AF-algebras is constructed. The construction is based on a representation of the Teichmueller space of a curve by the measured foliations due to…