Results 31 to 40 of about 167 (143)

Lectures on Graded Differential Algebras and Noncommutative Geometry [PDF]

, 2001
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments.
openaire   +3 more sources

Noncommutative polygonal cluster algebras

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein–Retakh, and are inspired by the emerging theory of Θ$\Theta$‐positivity for the groups Spin(p,q)$\mathrm{Spin}(p,q)$.
Zachary Greenberg, Dani Kaufman, Merik Niemeyer, Anna Wienhard   +3 more
wiley   +1 more source

Finite group gauge theory on graphs and gravity-like modes

Nuclear Physics B
We study gauge theory with finite group G on a graph X using noncommutative differential geometry and Hopf algebra methods with G-valued holonomies replaced by gauge fields valued in a ‘finite group Lie algebra’ subset of the group algebra CG ...
Shahn Majid, Francisco Simão
doaj   +1 more source

Noncommutative Geometry in the Framework of Differential Graded Categories [PDF]

, 2010
19 pages.
openaire   +4 more sources

Traces of Hecke operators on Drinfeld modular forms for GL2(Fq[T])$\operatorname{GL}_2(\mathbb {F}_q[T])$

Mathematika, Volume 72, Issue 2, April 2026.
Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
wiley   +1 more source

Negativity‐preserving transforms of tuples of symmetric matrices

Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.
Abstract Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining recent advances in matrix analysis with some novel arguments relying on well‐chosen test matrices, Sidon ...
Alexander Belton, Dominique Guillot, Apoorva Khare, Mihai Putinar   +3 more
wiley   +1 more source

Differential and Complex Geometry of Two-Dimensional Noncommutative Tori

Letters in Mathematical Physics, 2002
In [\textit{A. Schwarz}, Lett. Math. Phys. 58, 81-90 (2001; Zbl 1032.53082)], complex geometry of noncommutative tori and of projective modules over them in connection with noncommutative generalization of theta-functions are studied. In this paper, general results are illustrated using examples of two-dimensional tori.
Dieng, Momar, Schwarz, Albert
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Quantization of infinitesimal braidings and pre‐Cartier quasi‐bialgebras

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract In this paper, we extend Cartier's deformation theorem of braided monoidal categories admitting an infinitesimal braiding to the nonsymmetric case. The algebraic counterpart of these categories is the notion of a pre‐Cartier quasi‐bialgebra, which extends the well‐known notion of quasi‐triangular quasi‐bialgebra given by Drinfeld.
Chiara Esposito, Andrea Rivezzi, Jonas Schnitzer, Thomas Weber   +3 more
wiley   +1 more source

Einstein-Riemann Gravity on Deformed Spaces

Symmetry, Integrability and Geometry: Methods and Applications, 2006
A differential calculus, differential geometry and the E-R Gravity theory are studied on noncommutative spaces. Noncommutativity is formulated in the star product formalism. The basis for the gravity theory is the infinitesimal algebra of diffeomorphisms.
Julius Wess
doaj  

Ramanujan–Santos–Sales Hypermodular Operator Theorem and Spectral Kernels for Geometry-Adaptive Neural Operators in Anisotropic Besov Spaces

Axioms
We present Hyperbolic Symmetric Hypermodular Neural Operators (ONHSH), a novel operator learning framework for solving partial differential equations (PDEs) in curved, anisotropic, and modularly structured domains.
Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales   +1 more
doaj   +1 more source