Results 1 to 10 of about 1,518 (237)
Dirac Geometry I: Commutative Algebra [PDF]
Peking Mathematical Journal, 2023 Abstract The purpose of this paper and its sequel is to develop the geometry built from the commutative algebras that naturally appear as the homology of differential graded algebras and, more generally, as the homotopy of algebras in spectra.
Lars Hesselholt, Piotr Pstrągowski
openalex +3 more sources
Unitary Howe dualities in fermionic and bosonic algebras and related Dirac operators [PDF]
SciPost Physics Proceedings, 2023 In this paper we use the canonical complex structure $\mathbb{J}$ on $\mathbb{R}^{2n}$ to introduce a twist of the symplectic Dirac operator. This can be interpreted as the bosonic analogue of the Dirac operators on a Hermitian manifold.
Guner Muarem
doaj +2 more sources
Dirac cohomology for graded affine Hecke algebras [PDF]
Acta Mathematica, 2012 22 ...
Dan Barbasch +2 more
openalex +5 more sources
Virasoro Symmetry Algebra of Dirac Soliton Hierarchy [PDF]
Inverse Problems, 1996 8 pages, latex, to appear in Inverse ...
Wen‐Xiu Ma, Kam-Shun Li
openalex +3 more sources
Dirac Operators for the Dunkl Angular Momentum Algebra [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2022 We define a family of Dirac operators for the Dunkl angular momentum algebra depending on certain central elements of the group algebra of the Pin cover of the Weyl group inherent to the rational Cherednik algebra. We prove an analogue of Vogan's conjecture for this family of operators and use this to show that the Dirac cohomology, when non-zero ...
Kieran Calvert, Marcelo De Martino
openalex +5 more sources
Hopf–Hecke algebras, infinitesimal Cherednik algebras, and Dirac cohomology [PDF]
Pure and Applied Mathematics Quarterly, 2021 Hopf-Hecke algebras and Barbasch-Sahi algebras were defined by the first named author (2016) in order to provide a general framework for the study of Dirac cohomology. The aim of this paper is to explore new examples of these definitions and to contribute to their classification. Hopf-Hecke algebras are distinguished by an orthogonality condition and a
Flake, Johannes, Sahi, Siddhartha
openaire +3 more sources
Covariantization of quantized calculi over quantum groups [PDF]
Mathematica Bohemica, 2020 We introduce a method for construction of a covariant differential calculus over a Hopf algebra $A$ from a quantized calculus $da=[D,a]$, $a\in A$, where $D$ is a candidate for a Dirac operator for $A$.
Seyed Ebrahim Akrami, Shervin Farzi
doaj +1 more source
The Dirac Sea, T and C Symmetry Breaking, and the Spinor Vacuum of the Universe
Universe, 2021 We have developed a quantum field theory of spinors based on the algebra of canonical anticommutation relations (CAR algebra) of Grassmann densities in the momentum space. We have proven the existence of two spinor vacua.
Vadim Monakhov
doaj +1 more source
Dirac reductions and classical W-algebras
Journal of Mathematical Physics, 2023 In the first part of this paper, we generalize the Dirac reduction to the extent of non-local Poisson vertex superalgebra and non-local SUSY Poisson vertex algebra cases. Next, we modify this reduction so that we explain the structures of classical W-superalgebras and SUSY classical W-algebras in terms of the modified Dirac reduction.
Gahng Sahn Lee, Arim Song, Uhi Rinn Suh
openaire +2 more sources
The generalized relativistic harmonic oscillator with the Snyder-de Sitter algebra
Results in Physics, 2023 The Snyder-de Sitter (SdS) algebra is a model of non-commutative space–time admitting three fundamental parameters: the speed of light, the Planck mass and the cosmological constant, and therefore can be seen as an example of triply special relativity ...
A. Andolsi +3 more
doaj +1 more source