Score Title Author Discussions Created Updated
4-polytope Ciro Santilli 3702025-07-16
Regular 4-polytope Ciro Santilli 3702025-07-16
Tesseract Ciro Santilli 3702025-07-16
Differential geometry Ciro Santilli 3702025-07-16
Lie group Ciro Santilli 3702025-07-16
Lie derivative Ciro Santilli 3702025-07-16
Applications of Lie groups to differential equations Ciro Santilli 3702025-07-16
Lie algebra Ciro Santilli 3702025-07-16
Infinitesimal generator Ciro Santilli 3702025-07-16
Lie group-Lie algebra correspondence Ciro Santilli 3702025-07-16
Lie algebra exponential covering problem Ciro Santilli 3702025-07-16
A single exponential map is not enough to recover a simple Lie group from its algebra Ciro Santilli 3702025-07-16
The product of a exponential of the compact algebra with that of the non-compact algebra recovers a simple Lie from its algebra Ciro Santilli 3702025-07-16
Two different Lie groups can have the same Lie algebra Ciro Santilli 3702025-07-16
Every Lie algebra has a unique single corresponding simply connected Lie group Ciro Santilli 3702025-07-16
Universal covering group Ciro Santilli 3702025-07-16
Every Lie group that has a given Lie algebra is the image of an homomorphism from the universal cover group Ciro Santilli 3702025-07-16
Lie bracket Ciro Santilli 3702025-07-16
Exponential map Ciro Santilli 3702025-07-16
Exponential map (Lie theory) Ciro Santilli 3702025-07-16

Pinned article: Introduction to the OurBigBook Project

Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
  1. topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculus
    Articles of different users are sorted by upvote within each article page. This feature is a bit like:
    • a Wikipedia where each user can have their own version of each article
    • a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
    This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
    Figure 1.
    Screenshot of the "Derivative" topic page
    . View it live at: ourbigbook.com/go/topic/derivative
  2. local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:
    This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
    Figure 2.
    You can publish local OurBigBook lightweight markup files to either https://OurBigBook.com or as a static website
    .
    Figure 3.
    Visual Studio Code extension installation
    .
    Figure 4.
    Visual Studio Code extension tree navigation
    .
    Figure 5.
    Web editor
    . You can also edit articles on the Web editor without installing anything locally.
    Video 3.
    Edit locally and publish demo
    . Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.
    Video 4.
    OurBigBook Visual Studio Code extension editing and navigation demo
    . Source.
  3. https://raw.githubusercontent.com/ourbigbook/ourbigbook-media/master/feature/x/hilbert-space-arrow.png
  4. Infinitely deep tables of contents:
    Figure 6.
    Dynamic article tree with infinitely deep table of contents
    .
    Descendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact