Results 71 to 80 of about 19,016 (193)

A reduction theorem for the Character Triple Conjecture

Proceedings of the London Mathematical Society, Volume 131, Issue 4, October 2025.
Abstract In this paper, we show that the Character Triple Conjecture holds for all finite groups once assumed for all quasi‐simple groups. This answers the question on the existence of a self‐reducing form of Dade's conjecture, a problem that was extensively investigated by Dade in the 1990s.
Damiano Rossi
wiley   +1 more source

Global and microlocal aspects of Dirac operators: Propagators and Hadamard states

Mathematische Nachrichten, Volume 298, Issue 9, Page 2942-2974, September 2025.
Abstract We propose a geometric approach to construct the Cauchy evolution operator for the Lorentzian Dirac operator on Cauchy‐compact globally hyperbolic 4‐manifolds. We realize the Cauchy evolution operator as the sum of two invariantly defined oscillatory integrals—the positive and negative Dirac propagators—global in space and in time, with ...
Matteo Capoferri, Simone Murro
wiley   +1 more source

Investigating the motivational and knowledge affordances of conversational AI using induction, concretization and exemplification in math learning

British Journal of Educational Technology, Volume 56, Issue 5, Page 1814-1841, September 2025.
Abstract A promising approach to support students' math learning effectively, automatically and at scale within existing learning environments is conversational artificial intelligence (ConvAI). Although previous studies have suggested ConvAI's potential to guide, facilitate and enhance learning, its effects on students' conceptual change and academic ...
Chenglu Li, Bailing Lyu
wiley   +1 more source

Compositions of invertibility preserving maps for some monoids and their application to Clifford algebras

, 2018
For some monoids, we give a method of composing invertibility preserving maps associated to "partial involutions." Also, we define the notion of "determinants for finite dimensional algebras over a field." As examples, we give invertibility preserving ...
Yamaguchi, Naoya, Yamaguchi, Yuka
core  

Hecke-Clifford Algebras and Spin Hecke Algebras IV: Odd Double Affine Type

Symmetry, Integrability and Geometry: Methods and Applications, 2009
We introduce an odd double affine Hecke algebra (DaHa) generated by a classical Weyl group $W$ and two skew-polynomial subalgebras of anticommuting generators.
Ta Khongsap, Weiqiang Wang
doaj   +1 more source

Clifford Algebra with Mathematica [PDF]

, 2008
The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main ideas of Clifford algebra, with the main goal to develop a package for Clifford algebra calculations for the ...
Aragon-Camarasa, G., Aragon-Gonzalez, G., Aragon, J.L., Andrade, M.A.   +3 more
openaire   +2 more sources

Clifford Algebras and Possible Kinematics

Symmetry, Integrability and Geometry: Methods and Applications, 2007
We review Bacry and Lévy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous spacetimes for all ...
Alan S. McRae
doaj  

Representation of Integral Formulas for the Extended Quaternions on Clifford Analysis

Mathematics
This work addresses a significant gap in the existing literature by developing integral representation formulas for extended quaternion-valued functions within the framework of Clifford analysis. While classical Cauchy-type and Borel–Pompeiu formulas are
Ji Eun Kim
doaj   +1 more source

Circles and Clifford Algebras [PDF]

Functional Analysis and Its Applications, 2004
Consider a smooth map from a neighborhood of the origin in a real vector space to a neighborhood of the origin in a Euclidean space. Suppose that this map takes all germs of lines passing through the origin to germs of Euclidean circles, or lines, or a point. We prove that under some simple additional assumptions this map takes all lines passing though
openaire   +2 more sources

Square Root of a Multivector of Clifford Algebras in 3D: A Game with Signs

Mathematics
An algorithm is presented to extract the square root from a multivector (MV) in real Clifford algebras Clp,q, where n=p+q≤3, in radicals. It is shown that in Cl3,0, Cl1,2, and Cl0,3 algebras, there are up to four isolated square roots in a case of the ...
Arturas Acus, Adolfas Dargys
doaj   +1 more source