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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

The Hidden Geometry of the Quantum Euclidean Space

, 1998
We briefly describe how to introduce the basic notions of noncommutative differential geometry on the 3-dim quantum space covariant under the quantum group of rotations $SO_q(3)$.Comment: latex file, 9 pages, no figure.
Fiore, Gaetano, Madore, John
core   +1 more source

Average‐Case Matrix Discrepancy: Satisfiability Bounds

Random Structures &Algorithms, Volume 67, Issue 3, October 2025.
ABSTRACT Given a sequence of d×d$$ d\times d $$ symmetric matrices {Wi}i=1n$$ {\left\{{\mathbf{W}}_i\right\}}_{i=1}^n $$, and a margin Δ>0$$ \Delta >0 $$, we investigate whether it is possible to find signs (ε1,…,εn)∈{±1}n$$ \left({\varepsilon}_1,\dots, {\varepsilon}_n\right)\in {\left\{\pm 1\right\}}^n $$ such that the operator norm of the signed sum ...
Antoine Maillard
wiley   +1 more source

Differentials of Higher Order in Noncommutative Differential Geometry

Letters in Mathematical Physics, 1997
In differential geometry, the notation d^n f along with the corresponding formalism has fallen into disuse since the birth of exterior calculus. However, differentials of higher order are useful objects that can be interpreted in terms of functions on iterated tangent bundles (or in terms of jets).
openaire   +3 more sources

Cohomological Operators and Covariant Quantum Superalgebras

, 2003
We obtain an interesting realization of the de Rham cohomological operators of differential geometry in terms of the noncommutative q-superoscillators for the supersymmetric quantum group GL_{qp} (1|1).
Ardalan F, Aref'eva I Ya, Castellani L, Connes A, Costerina P, Douglas M R, Drinfeld V G, Faddeev L D, Falomir H, Ghosh S, Harikumar E, Jimbo M, Jimbo M, Klemm A, Majid S, Malik R P, Malik R P, Malik R P, Malik R P, Manin Yu I, Mukhi S, Nishijima K, Nishijima K, R P Malik, Schmidke W B, Seiberg N, Sheikh-Jabbari M M, Tanaka S, Wess J, Witten E, Woronowicz S L   +30 more
core   +1 more source

Compressibility Function and Speed of Sound in the Non‐Commutative Quantum Hadrodynamics Type‐I Model for Neutron Stars

Astronomische Nachrichten, Volume 346, Issue 7-8, September 2025.
ABSTRACT We investigate the effects of a minimal measurable length on neutron stars, within the quantum hadrodynamics (QHD‐I) model modified by the Generalized Uncertainty Principle (GUP). Working in a deformed Poisson algebra framework, we incorporate GUP effects via a time‐invariant transformation of the phase space volume, effectively reducing the ...
João Gabriel Galli Gimenez, Dimiter Hadjimichef, César A. Zen Vasconcellos   +2 more
wiley   +1 more source

Twisting of quantum differentials and the Planck scale Hopf algebra

, 1998
We show that the crossed modules and bicovariant different calculi on two Hopf algebras related by a cocycle twist are in 1-1 correspondence. In particular, for quantum groups which are cocycle deformation-quantisations of classical groups the calculi ...
Majid, Shahn, Oeckl, Robert
core   +1 more source

Functorial constructions related to double Poisson vertex algebras

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract For any double Poisson algebra, we produce a double Poisson vertex algebra using the jet algebra construction. We show that this construction is compatible with the representation functor which associates to any double Poisson (vertex) algebra and any positive integer a Poisson (vertex) algebra.
Tristan Bozec, Maxime Fairon, Anne Moreau   +2 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
openaire   +4 more sources

Structural Properties of The Clifford–Weyl Algebra ${𝒜}_q^{\pm }$

Mathematics
The Clifford–Weyl algebra 𝒜q±, as a class of solvable polynomial algebras, combines the anti-commutation relations of Clifford algebras 𝒜q+ with the differential operator structure of Weyl algebras 𝒜q−. It exhibits rich algebraic and geometric properties.
Jia Zhang, Gulshadam Yunus
doaj   +1 more source