Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Poisson's And Laplace's Equation01:25

Poisson's And Laplace's Equation

4.4K
The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.
4.4K
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

1.5K
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
1.5K
Fundamental Theorem of Algebra01:30

Fundamental Theorem of Algebra

324
The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as:  with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the...
324
SFG Algebra01:16

SFG Algebra

358
In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...
358
Poisson Probability Distribution01:09

Poisson Probability Distribution

12.2K
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
12.2K
Poisson's Ratio01:23

Poisson's Ratio

1.6K
Poisson's ratio is a material property that indicates their stress response. It explains the connection between the elongation or compression a material undergoes in the direction of an applied force and the contraction or expansion it experiences perpendicular to that force. When a slender bar is loaded axially, it stretches in the direction of the force and contracts laterally. Poisson's ratio is the negative ratio of this lateral contraction to the axial elongation. The negative sign...
1.6K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Lorentzian bordisms in algebraic quantum field theory.

Letters in mathematical physics·2025
Same journal

Differentiability and other properties of the cosmological volume function.

Letters in mathematical physics·2026
Same journal

Ground state energy of a dilute Bose gas with three-body hard-core interactions.

Letters in mathematical physics·2026
Same journal

Approximation of magnetic Schrödinger operators with <math><mi>δ</mi></math> -interactions supported on networks.

Letters in mathematical physics·2026
Same journal

The flea on the Magnetic Elephant.

Letters in mathematical physics·2026
Same journal

Normal typicality and dynamical typicality for a random block-band matrix model.

Letters in mathematical physics·2025
Same journal

Lagrangian multiforms and dispersionless integrable systems.

Letters in mathematical physics·2025
See all related articles

Related Experiment Video

Updated: Feb 24, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K

Shifted Poisson structures on higher Chevalley-Eilenberg algebras.

Cameron Kemp1, Robert Laugwitz1, Alexander Schenkel1,2

  • 1School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD UK.

Letters in Mathematical Physics
|February 23, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a graphical calculus for n-shifted Poisson structures on differential graded algebras. It extends findings on Lie algebras to Lie 2-algebras, revealing new structures related to higher quantum groups.

Keywords:
Derived algebraic geometryShifted poisson structures

More Related Videos

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
10:35

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

12.8K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

9.0K

Related Experiment Videos

Last Updated: Feb 24, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.8K
Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
10:35

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials

Published on: September 26, 2014

12.8K
Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids
08:04

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

Published on: May 27, 2020

9.0K

Area of Science:

  • Algebraic Topology
  • Mathematical Physics
  • Differential Geometry

Background:

  • Commutative differential graded algebras are fundamental in algebraic topology and mathematical physics.
  • Poisson structures and their generalizations (n-shifted Poisson structures) are crucial for understanding classical and quantum systems.
  • Lie algebras and Lie 2-algebras provide frameworks for describing symmetries in various physical theories.

Purpose of the Study:

  • To develop a novel graphical calculus for determining n-shifted Poisson structures.
  • To analyze these structures on finitely generated semi-free commutative differential graded algebras.
  • To generalize existing results from Lie algebras to Lie 2-algebras.

Main Methods:

  • Development of a graphical calculus tailored for n-shifted Poisson structures.
  • Application of the calculus to the Chevalley-Eilenberg algebra of Lie algebras and Lie 2-algebras.
  • Comparison and extension of Safronov's results for n=1 and n=2 shifted Poisson structures.

Main Results:

  • The graphical calculus successfully determines n-shifted Poisson structures on the specified algebras.
  • For ordinary Lie algebras, the (n=1) and (n=2) shifted Poisson structures correspond to quasi-Lie bialgebra structures and invariant symmetric tensors, respectively.
  • Generalization to Lie 2-algebras yields n-shifted Poisson structures for n in {1, 2, 3, 4}, interpreted as semi-classical data of higher quantum groups.

Conclusions:

  • The developed graphical calculus offers a powerful tool for studying n-shifted Poisson structures.
  • The findings extend the understanding of Poisson structures to higher algebraic structures like Lie 2-algebras.
  • This work provides a bridge between algebraic structures and the semi-classical data of higher quantum groups.